%% Theory of Computing
%% File: gs010.bib
%% Publication date: May 31, 2025
%% Authors: Markus Blaeser and Christian Ikenmeyer
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@incollection{Aar:16,
author="Aaronson, Scott",
editor="Nash, Jr., John Forbes and Rassias, Michael Th.",
title="{P} $\stackrel{?}{=}$ {NP}",
booktitle="Open Problems in Mathematics",
year="2016",
publisher= springer,
pages={1--122},
doi="10.1007/978-3-319-32162-2\_1",
}
%
%
#OK
@article{Aar:17,
author="Aaronson, Scott",
title="{P} $\stackrel{?}{=}$ {NP}",
journal = eccc,
Year = {2017},
volume = {TR17-004},
eprint = {ecccprimary:TR17-004},
}
%
%
@phdthesis{alder,
author = {Alexander Alder},
title = {Grenzrang und {G}renzkomplexit\"at aus algebraischer und topologischer {S}icht},
school = {Zurich University},
year = 1984,
}
%
#OK
@article{DBLP:journals/cc/AllenderW16,
author    = {Eric Allender and Fengming Wang},
title     = {On the power of algebraic branching programs of width two},
journal   = ccomplex,
volume    = {25},
number    = {1},
pages     = {217--253},
year      = {2016},
doi       = {10.1007/s00037-015-0114-7},
}
%
%
%
@article{BS:83,
title={The complexity of partial derivatives},
author={Baur, Walter and Strassen, Volker},
journal= tcs,
volume={22},
number={3},
pages={317--330},
year={1983},
doi={10.1016/0304-3975(83)90110-X},
}
%
#OK
@article{DBLP:journals/siamcomp/Ben-OrC92,
author    = {Michael Ben{-}Or and Richard Cleve},
title     = {Computing Algebraic Formulas Using a Constant Number of Registers},
journal   = sicomp,
volume    = {21},
number    = {1},
pages     = {54--58},
year      = {1992},
doi       = {10.1137/0221006},
}
%
%
%
%
@article{BinCapLot+:IPL79,
author = {Bini, Dario and Capovani, Milvio and Lotti, Grazia and Romani, Francesco},
title = {${O}(n^{2.7799})$ complexity for $n\times n$ matrix multiplication},
journal = ipl,
volume = {8},
number=5,
year = {1979},
pages = {234--235},
doi={10.1016/0020-0190(79)90113-3},
}
%
@Article{Bla:00,
author={Bl{\"a}ser, Markus},
title={Lower bounds for the bilinear complexity of associative algebras},
journal= ccomplex,
year={2000},
volume={9},
number={2},
pages={73--112},
doi={10.1007/PL00001605},
}
%
%
@inproceedings{DBLP:conf/cocoon/Blaser01,
author    = {Markus Bl{\"{a}}ser},
title  = {Complete Problems for {V}aliant's Class of qp-Computable Families of
Polynomials},
crossref = {pcocoon01},
pages     = {1--10},
doi       = {10.1007/3-540-44679-6\_1},
}
%
#OK
%
@book{DBLP:journals/toc/Blaser13,
author = {Bl{\"a}ser, Markus},
title = {Fast Matrix Multiplication},
year = {2013},
pages = {1--60},
publisher = toclib,
number = {5},
series = {Graduate Surveys},
doi = {10.4086/toc.gs.2013.005},
}
%
%
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@unpublished{BI:17,
author={Markus Bl{\"{a}}ser and Christian Ikenmeyer},
title={Lecture Notes for {G}eometric {C}omplexity {T}heory 2 (unpublished)},
note={Available at \href{https://www.dcs.warwick.ac.uk/~u2270030/teaching_sb/winter1718/gct2/index.html}{U. Warwick}},
}
%
#OK
@inproceedings{DBLP:conf/stoc/BlaserIJL18,
author    = {Markus Bl{\"{a}}ser and
Christian Ikenmeyer and
Gorav Jindal and
Vladimir Lysikov},
title     = {Generalized matrix completion and algebraic natural proofs},
crossref   = {pstoc18},
pages     = {1193--1206},
doi       = {10.1145/3188745.3188832},
}
%
#OK
@inproceedings{DBLP:conf/coco/BlaserIMPS20,
author    = {Markus Bl{\"{a}}ser and
Christian Ikenmeyer and
Meena Mahajan and
Anurag Pandey and
Nitin Saurabh},
title  = {Algebraic Branching Programs, Border Complexity, and Tangent Spaces},
crossref = {pccc20},
pages     = {21:1--24},
doi       = {10.4230/LIPIcs.CCC.2020.21},
}
%
#OK
@article{DBLP:journals/jacm/Brent74,
author    = {Richard P. Brent},
title  = {The Parallel Evaluation of General Arithmetic Expressions},
journal   = jacm,
volume    = {21},
number    = {2},
pages     = {201--206},
year      = {1974},
doi       = {10.1145/321812.321815},
}
%
#OK
@article{DBLP:journals/jacm/BringmannIZ18,
author    = {Karl Bringmann and Christian Ikenmeyer and Jeroen Zuiddam},
title     = {On Algebraic Branching Programs of Small Width},
journal   = jacm,
volume    = {65},
number    = {5},
pages     = {32:1--29},
year      = {2018},
doi       = {10.1145/3209663},
}
%
%
%
@book{Buergisser:Completeness,
author = {Peter B{\"u}rgisser},
title = {Completeness and Reduction in Algebraic Complexity Theory},
publisher = springer,
year = {2000},
doi={10.1007/978-3-662-04179-6},
}
%
%
@article{bci:10,
author = {Peter B\"urgisser and Matthias Christandl and Christian Ikenmeyer},
title = "Even partitions in plethysms",
journal = jalgebra,
volume = "328",
number = "1",
pages = "322--329",
year = "2011",
doi = "10.1016/j.jalgebra.2010.10.031",
}
%
%
%
%
@book{BCS,
title = {Algebraic Complexity Theory},
author = {Peter B\"urgisser and Michael Clausen and M.~Amin Shokrollahi},
publisher = springer,
year = {1997},
doi={10.1007/978-3-662-03338-8},
}
%
%
@inproceedings{BI:10,
author    = {Peter B{\"u}rgisser and Christian Ikenmeyer},
title     = {Geometric Complexity Theory and Tensor Rank},
crossref  = {pstoc11},
PAGES = {509--518},
doi={10.1145/1993636.1993704},
}
%
%
%
%
%
@inproceedings{BI:13,
author    = {Peter B{\"u}rgisser and Christian Ikenmeyer},
title     = {Explicit Lower Bounds via Geometric Complexity Theory},
crossref  = {pstoc13},
PAGES = {141--150},
doi={10.1145/2488608.2488627},
}
%
%
%
#OK
@article{BI:17b,
title = "Fundamental invariants of orbit closures",
author = "Peter B{\"u}rgisser and Christian Ikenmeyer",
journal = jalgebra,
volume = "477",
pages = "390--434",
year = "2017",
doi = "10.1016/j.jalgebra.2016.12.035",
}
%
%
%
@article{BIP:16,
author = {Peter B{\"u}rgisser and Christian Ikenmeyer and Greta Panova},
title = {No occurrence obstructions in geometric complexity theory},
journal = jams,
volume =  32,
number = 1, 
pages = {163--193},
year = {2019},
note   = {\prelim \href{https://doi.org/10.1109/FOCS.2016.49}{FOCS'16}},
doi={10.1090/jams/908},
}
%
%
%
%
@article{BLMW:11,
author = {B\"urgisser, Peter and Landsberg, Joseph M. and Manivel, Laurent
 and Weyman, Jerzy},
journal =       sicomp,
pages =         {1179--1209},
title =         {An overview of mathematical issues arising in the
geometric complexity theory approach to {VP} $\neq$ {VNP}},
volume =        {40},
number   =       4,
year =          {2011},
doi={10.1137/090765328},
}
%
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@inproceedings{CLP:21,
author =   {Prasad Chaugule and Nutan Limaye and Shourya Pandey},
title =    {Variants of the Determinant polynomial and {VP}-completeness},
crossref = {pcsr21},
pages = {31--55},
doi={10.1007/978-3-030-79416-3\_3},
}
%
%
%
@article{CWK:11,
author={Xi Chen and Neeraj Kayal and Avi Wigderson},
year={2011},
volume={6},
journal=FoundTrendsTCS,
title={Partial Derivatives in Arithmetic Complexity and Beyond},
number={1--2},
pages={1--138},
doi={10.1561/0400000043},
}
%
%
%
@inproceedings{Coo:00,
author =        {Stephen Cook},
booktitle =     {The Millennium Prize Problems},
title =         {The {P} versus {N}{P} problem},
publisher = {Clay Mathematical Institute and American Mathematical Society},
year =          {2000},
note = {Available at \href{https://bookstore.ams.org/MPRIZE}{AMS Bookstore}},
}
%
#OK
@article{DBLP:journals/siamcomp/CoppersmithW82,
author    = {Don Coppersmith and Shmuel Winograd},
title     = {On the Asymptotic Complexity of Matrix Multiplication},
journal   = sicomp,
volume    = {11},
number    = {3},
pages     = {472--492},
year      = {1982},
doi       = {10.1137/0211038},
}
%
@book{DBLP:books/daglib/0023376,
author    = {Thomas H. Cormen and Charles E. Leiserson and Ronald L. Rivest and Clifford Stein},
title     = {Introduction to Algorithms},
edition = {3rd}, 
publisher = {{MIT} Press},
year      = {2009},
url       = {Available at \href{https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/}{MIT press}},
}
%
#OK
%
@article{DBLP:journals/siamcomp/Csanky76,
author    = {L{\'a}szl{\'o} Cs{\'a}nky},
title     = {Fast Parallel Matrix Inversion Algorithms},
journal   = sicomp,
volume    = {5},
number    = {4},
pages     = {618--623},
year      = {1976},
doi       = {10.1137/0205040},
}
%
%
#OK
@article{DBLP:conf/fsttcs/DurandMMRS14,
author    = {Arnaud Durand and Meena Mahajan and Guillaume Malod and Nicolas de Rugy{-}Altherre and Nitin Saurabh},
title     = {Homomorphism Polynomials Complete for {VP}},
journal=cjtcs,
volume=2016,
year=2016,
number=3,
note ={\prelim \href{https://doi.org/10.4230/LIPIcs.FSTTCS.2014.493}{FSTTCS'14}},
}
%
@inproceedings{EGOW:18,
author ={Klim Efremenko and Ankit Garg and Rafael Oliveira and Avi Wigderson},
title ={Barriers for Rank Methods in Arithmetic Complexity},
crossref = {pitcs18},
pages ={1:1--19},
doi ={10.4230/LIPIcs.ITCS.2018.1},
}
%
%
#OK
%
@article{Fis:94,
author = {Ismor Fischer},
title = {Sums of Like Powers of Multivariate Linear Forms},
journal = mathmagazine,
number = {1},
pages = {59-61},
volume = {67},
year = {1994},
doi = {10.2307/2690560},
}
%
@article{For:09,
address =       {New York, NY, USA},
author =        {Fortnow, Lance},
journal =       {Commun. ACM},
number =        {9},
pages =         {78--86},
publisher =     {ACM},
title =         {The status of the {P} versus {N}{P} problem},
volume =        {52},
year =          {2009},
doi =           {10.1145/1562164.1562186},
}
%
%
%
@article {fro:1897,
AUTHOR = {Georg Ferdinand Frobenius},
TITLE = {{\"U}ber die {D}arstellung der endlichen {G}ruppen durch lineare {S}ubstitutionen},
JOURNAL = {Sitzungsberichte der K\"oniglich Preussischen Akademie der Wissenschaften zu Berlin},
YEAR = {1897},
PAGES = {994-1015},
doi={10.3931/e-rara-18879},
}
%
%
%
%
@book {fult:97,
AUTHOR = {William Fulton},
TITLE = {Young Tableaux},
PUBLISHER = cup,
YEAR = {1996},
doi={10.1017/CBO9780511626241},
}
%
#OK
%
@inproceedings{GMOW:19,
author = {Ankit Garg and Visu Makam and Rafael Oliveira and Avi Wigderson},
title = {More Barriers for Rank Methods, via a ``numeric to Symbolic'' Transfer},
crossref = {pfocs19},
pages = {824--844},
doi = {10.1109/FOCS.2019.00054},
}
%
%
%
@Article{Gay:76,
author= {Gay, David A.},
title= {Characters of the {W}eyl group of {$SU(n)$} on zero weight
spaces and centralizers of permutation representations},
journal= rocky,
volume= {6},
year= {1976},
number= {3},
pages= {449--455},
note = {\href{https://www.jstor.org/stable/44236121}{JSTOR}},
}
%
%
#OK
@Article{GMP:14,
author={Grigoriev, Dima and Muzychuk, Mikhail and Ponomarenko, Ilya},
title={Tensor rank: {M}atching polynomials and {S}chur rings},
journal= FoundComputMath,
year={2014},
volume={14},
number={3},
pages={457--481},
doi={10.1007/s10208-014-9190-3},
}
%
%
@phdthesis{Gro:12,
author =        {Grochow, Joshua A.},
school =        {Department of Computer Science, University of
Chicago},
title =         {Symmetry and equivalence relations in classical and
geometric complexity theory},
year =          {2012},
note={Available at \href{https://home.cs.colorado.edu/~jgrochow/grochow-thesis.pdf}{author's website}}
}
%
#OK
@article{DBLP:journals/cc/Grochow15,
author    = {Joshua A. Grochow},
title     = {Unifying Known Lower Bounds via Geometric Complexity Theory},
journal   = ccomplex,
volume    = {24},
number    = {2},
pages     = {393--475},
year      = {2015},
doi       = {10.1007/s00037-015-0103-x},
}
%
@inproceedings{DBLP:conf/icalp/GrochowMQ16,
author = {Joshua A. Grochow and Ketan D. Mulmuley and Youming Qiao},
title     = {Boundaries of {VP} and {VNP}},
crossref   = {picalp16},
pages     = {34:1--14},
year      = {2016},
doi       = {10.4230/LIPIcs.ICALP.2016.34},
}
%
#OK
@article{DBLP:journals/jal/Hastad90,
author    = {Johan H{\aa}stad},
title     = {Tensor Rank is {NP}-Complete},
journal   = JAlgorithms,
volume    = {11},
number    = {4},
pages     = {644--654},
year      = {1990},
doi       = {10.1016/0196-6774(90)90014-6},
}
%
%
@article {How:87,
AUTHOR = {Howe, Roger},
TITLE = {{$({\rm GL}_n,{\rm GL}_m)$}-duality and symmetric plethysm},
JOURNAL = {Proc. Indian Acad. Sci. Math. Sci.},
FJOURNAL = {Indian Academy of Sciences. Proceedings. Mathematical Sciences},
VOLUME = {97},
YEAR = {1987},
NUMBER = {1--3},
PAGES = {85--109},
DOI = {10.1007/BF02837817},
}
%
#OK
@article{HL:16,
title = "The boundary of the orbit of the 3-by-3 determinant polynomial",
author = {Jesko H\"uttenhain and Pierre Lairez},
journal = ComptesRendus,
volume = "354",
number = "9",
pages = "931--935",
year = "2016",
doi = "https://doi.org/10.1016/j.crma.2016.07.002",
}
%
%
@phdthesis{ike:12b,
author =        {Christian Ikenmeyer},
note =          {Online available at
\href{http://nbn-resolving.de/urn:nbn:de:hbz:466:2-10472}{U. Paderborn}},
school =        {Institute of Mathematics, University of Paderborn},
title =         {Geometric Complexity Theory, Tensor Rank, and
{L}ittlewood-{R}ichardson Coefficients},
year =          {2012},
}
%
%
%
@article{IP:15,
author = {Christian Ikenmeyer and Greta Panova},
title = {Rectangular {K}ronecker coefficients and plethysms in geometric complexity theory},
journal   = AdvMath,
volume = 319,
pages = {40--66},
year = {2017},
note = {\prelim \href{https://doi.org/10.1109/FOCS.2016.50}{FOCS'16}},
doi={10.1016/j.aim.2017.08.024},
}
%
%
@article {kadish-landsberg:14,
AUTHOR = {Kadish, Harlan and Landsberg, Joseph M.},
TITLE = {Padded polynomials, their cousins, and geometric complexity
theory},
JOURNAL = {Comm. Algebra},
FJOURNAL = {Communications in Algebra},
VOLUME = {42},
YEAR = {2014},
NUMBER = {5},
PAGES = {2171--2180},
DOI = {10.1080/00927872.2012.758268},
}
%
@unpublished{Knu:17,
author =        {Allen Knutson},
note =          {{MathOverflow} post: \url{https://mathoverflow.net/questions/267552/peter-weyl-vs-schur-weyl-theorem}},
title =         {Peter-{W}eyl vs. {S}chur-{W}eyl theorem},
year =          {2017},
}
%
%
%
@book{kowalski,
title = {An Introduction to the Representation Theory of Groups},
author = {Emmanuel Kowalski},
year = 2014,
publisher = ams,
doi={10.1090/gsm/155},
}
%
%
%
@book{Kra:85,
author = {Kraft, Hanspeter},
title = {Geometrische {M}ethoden in der {I}nvariantentheorie},
year = {1985},
PUBLISHER = {Friedr. Vieweg und Sohn Verlagsgesellschaft},
ADDRESS = {Braunschweig},
ISBN = {3-528-18525-2},
doi={10.1007/978-3-322-83813-1},
}
%
#OK
%
@article{Lan:14,
author = {Landsberg, Joseph M.},
title = {New Lower Bounds for the Rank of Matrix Multiplication},
journal = sicomp,
volume = {43},
number = {1},
pages = {144--149},
year = {2014},
doi = {10.1137/120880276},
}
%
%
@article{Lan:13,
author={Landsberg, Joseph M.},
title={Geometric complexity theory: an introduction for geometers},
journal={Annali dell' Universit\`a di Ferrara},
year={2015},
volume={61},
number={1},
pages={65-117},
doi={10.1007/s11565-014-0202-7},
}
%
%
@book{Lan:17,
author={Landsberg, Joseph M.},
title={Geometry and Complexity Theory},
DOI={10.1017/9781108183192},
publisher= cup,
year={2017},
}
%
%
%
%
@article{LanManRes13,
title = {Hypersurfaces with degenerate duals and the {Geometric Complexity Theory Program}},
author = {Joseph M. Landsberg and Laurent Manivel and Nicolas Ressayre},
journal = CommMathHelv,
volume = 88,
number=2,
year = 2013,
pages = {469--484},
doi={10.4171/CMH/292},
}
%
%
#OK
@article{LM:18,
author = {Landsberg, Joseph M. and Micha\l{}ek, Mateusz},
title = "{A $2n^2-\log_2(n)-1$ lower bound for the border rank of matrix multiplication}",
journal = InternatMathRes,
volume = {2018},
number = {15},
pages = {4722--4733},
year = {2018},
doi = {10.1093/imrn/rnx025},
}
%
#OK
@article{LO:15,
author = {Landsberg, Joseph M. and Ottaviani, Giorgio},
title = {New Lower Bounds for the Border Rank of Matrix Multiplication},
journal = toc,
year = {2015},
pages = {285--298},
volume = {11},
number = {11},
doi = {10.4086/toc.2015.v011a011},
}
%
%
%
#OK
%
%
%
@article {LP:90,
AUTHOR = {Michael J. Larsen and Richard Pink},
TITLE = {Determining representations from invariant dimensions},
JOURNAL = inventiones,
VOLUME = {102},
number=2,
YEAR = {1990},
PAGES = {377--398},
doi = {10.1007/BF01233432},
}
%
#OK
@article{DBLP:journals/mst/MahajanS18,
author    = {Meena Mahajan and Nitin Saurabh},
title     = {Some Complete and Intermediate Polynomials in Algebraic Complexity
Theory},
journal   = ThyCompSys,
volume    = {62},
number    = {3},
pages     = {622--652},
year      = {2018},
doi       = {10.1007/s00224-016-9740-y},
}
%
%
#OK
%
%
@article{DBLP:journals/cjtcs/MahajanV97,
author    = {Meena Mahajan and V. Vinay},
title  = {Determinant: Combinatorics, Algorithms, and Complexity},
journal   = cjtcs,
volume    = 1997,
year=1997,
number    = 5,
doi       = {10.4086/cjtcs.1997.005},
}
%
#OK
@article{DBLP:journals/jc/MalodP08,
author    = {Guillaume Malod and Natacha Portier},
title  = {Characterizing {V}aliant's algebraic complexity classes},
journal   = jcomplexity,
volume    = {24},
number    = {1},
pages     = {16--38},
year      = {2008},
doi       = {10.1016/j.jco.2006.09.006},
}
%
#OK
@article{Mul:11,
address =       {New York, NY, USA},
author =        {Mulmuley, Ketan D.},
journal =       jacm,
number =        {2},
pages =         {5:1--26},
title =         {On {P} vs. {N}{P} and geometric complexity theory:
Dedicated to {S}ri {R}amakrishna},
volume =        {58},
year =          {2011},
doi =           {10.1145/1944345.1944346},
}
%
%
%
@article {MS:01,
AUTHOR = {Mulmuley, Ketan D. and Sohoni, Milind},
TITLE = {Geometric complexity theory. {I}. {A}n approach to the {P} vs.\ {NP} and related problems},
JOURNAL = sicomp,
VOLUME = {31},
YEAR = {2001},
NUMBER = {2},
PAGES = {496--526},
doi={10.1137/S009753970038715X},
}
%
%
#OK
@article {MS:08,
AUTHOR = {Mulmuley, Ketan D. and Sohoni, Milind},
TITLE = {Geometric complexity theory~{II}: {T}owards explicit obstructions for embeddings among class varieties},
JOURNAL = sicomp,
VOLUME = {38},
YEAR = {2008},
NUMBER = {3},
PAGES = {1175--1206},
DOI = {10.1137/080718115},
}
%
%
@book{Mum:95,
title= {Algebraic {G}eometry {I}: Complex {P}rojective {V}arieties},
author= {David B. Mumford},
series= {Classics in mathematics},
publisher= springer,
note= {Reprint of the 1976 edition in Grundlehren der
mathematischen Wissenschaften, vol. 221. Available at \href{https://link.springer.com/book/9783540586579}{Springer}},
year= {1995},
}
%
%
%
@unpublished{Nishiyama,
author={Kyo Nishiyama},
title={Restriction of the irreducible representations of {$\mathrm{GL}_n$} to the symmetric group $\mathfrak {S}_n$},
note={Unpublished preprint, online available at \href{http://rtweb.math.kyoto-u.ac.jp/home_kyo/preprint/glntosn.pdf}{Kyoto University}},
}
%
%
%
@incollection{Ost:54,
author = "Ostrowski, Alexander",
title = "On Two Problems in Abstract Algebra Connected with {H}orner's Rule",
booktitle = "Studies in Mathematics and Mechanics presented to Richard von Mises",
publisher = ap,
pages = "40--48",
year = "1954",
doi={10.1016/B978-1-4832-3272-0.50010-7},
}
%
%
%
@article{Reg:02,
author =        {Kenneth W. Regan},
journal =       {Bulletin of the EATCS},
pages =         {86--99},
title =  {Understanding the {M}ulmuley--{S}ohoni approach to {P} vs {N}{P}},
volume =        {78},
year =          {2002},
note = {Available at \href{https://cse.buffalo.edu/faculty/regan/papers/pdf/Reg02MSFD.pdf}{author's website}},
}
%
%
%
@article {remm:89,
AUTHOR = {Remmel, Jeffrey B.},
TITLE = {A formula for the {K}ronecker products of {S}chur functions of hook shapes},
JOURNAL = jalgebra,
VOLUME = {120},
YEAR = {1989},
NUMBER = {1},
PAGES = {100--118},
doi={10.1016/0021-8693(89)90191-9},
}
%
%
%
@article {rosa:01,
AUTHOR = {Rosas, Mercedes H.},
TITLE = {The {K}ronecker product of {S}chur functions indexed by two-row shapes or hook shapes},
JOURNAL = jaco,
VOLUME = {14},
YEAR = {2001},
NUMBER = {2},
PAGES = {153--173},
doi={10.1023/A:1011942029902},
}
%
#OK
%
@article{DBLP:journals/corr/SchaeferS16,
author    = {Marcus Schaefer and
Daniel {\v S}tefankovi{\v c}},
title     = {The Complexity of Tensor Rank},
journal   = ThyCompSys,
volume    = {62},
number    = {5},
pages     = {1161--1174},
year      = {2018},
doi       = {10.1007/s00224-017-9800-y},
}
%
#OK
@misc{shitov,
author    = {Yaroslav Shitov},
title     = {How hard is tensor rank?},
year      = {2016},
eprint = {1611.01559},
}
%
#OK
@inproceedings{DBLP:conf/soda/SongWZ19,
author    = {Zhao Song and
David P. Woodruff and
Peilin Zhong},
title     = {Relative Error Tensor Low Rank Approximation},
crossref   = {psoda19},
pages     = {2772--2789},
doi       = {10.1137/1.9781611975482.172},
}
%
%
@incollection {sta:00,
AUTHOR = {Stanley, Richard P.},
TITLE = {Positivity problems and conjectures in algebraic combinatorics},
editors={Vladimir Arnold and Michael Atiyah and Peter D. Lax and Barry Mazur},
BOOKTITLE = {Mathematics: {F}rontiers and perspectives},
PAGES = {295--319},
PUBLISHER = ams,
YEAR = {2000},
note ={Available at \href{https://math.mit.edu/~rstan/pubs/pubfiles/116.pdf}{author's website}},
}
%
#OK
%
@article{Strassen1987,
author = {Strassen, Volker},
journal = reine,
title = {Relative bilinear complexity and matrix multiplication},
volume = {375--376},
number = 4, 
pages = {406-443},
note = {Available at \href{http://eudml.org/doc/152921}{\emph{Eu}DML}},
year = {1987},
}
%
%
%
@article{Strassen:NM69,
author = {Strassen, Volker},
title = {Gaussian elimination is not optimal},
journal = NumerMath,
volume = {13},
year = {1969},
pages = {354--356},
doi={10.1007/BF02165411},
}
%
%
%
@article{Str:74,
author = {Strassen, Volker},
journal = sicomp,
pages =   {128--149},
title = {Polynomials with Rational Coefficients Which are Hard to Compute},
volume =        {3},
number =        {2},
year =          {1974},
doi={10.1137/0203010},
}
%
@inproceedings{DBLP:conf/approx/Swernofsky18,
author    = {Joseph Swernofsky},
title     = {Tensor Rank is Hard to Approximate},
crossref  = {papprox18},
pages     = {26:1--9},
doi       = {10.4230/LIPIcs.APPROX-RANDOM.2018.26},
}
%
%
%
%
@book {TY:05,
AUTHOR = {Tauvel, Patrice and Yu, Rupert W. T.},
TITLE = {Lie Algebras and Algebraic Groups},
PUBLISHER = springer,
YEAR = {2005},
doi={10.1007/b139060},
}
%
%
%
%
@incollection{Val:79b,
author =        {Valiant, Leslie G.},
crossref = {pstoc79},
pages =         {249--261},
title =         {Completeness classes in algebra},
year =          {1979},
doi={10.1145/800135.804419},
}
%
#OK
%
@article{VSBR:83,
author = {Valiant, Leslie G. and Skyum, Sven and Berkowitz, Stuart J. and Rackoff, Charles},
title = {Fast Parallel Computation of Polynomials Using Few Processors},
journal = sicomp,
volume = {12},
number = {4},
pages = {641-644},
year = {1983},
doi = {10.1137/0212043},
}
%
%
%
%
@article{Val:79,
title = {The Complexity of Computing the Permanent},
author = {Leslie G. Valiant},
journal = tcs,
pages = {189-201},
volume = {8},
number=2,
year = {1979},
doi={10.1016/0304-3975(79)90044-6},
}
%
#OK
@article{Yu:16,
author = "Yu, Jun",
journal = duke,
title = "On the dimension datum of a subgroup",
volume = "165",
year = "2016",
number = "14",
pages = "2683--2736",
doi =   "10.1215/00127094-3619898",
}
%
%
@unpublished{Bur:06,
	author={Peter B\"urgisser},
	title={\emph{{K}ombinatorik der {D}arstellungstheorie symmetrischer {G}ruppen}
({C}ombinatorics of the representation theory of symmetric groups)},
	note={Course held in 2006 at Paderborn University. 
	Handwritten course notes by Christian Ikenmeyer, unpublished}
}
%
%
@unpublished{Bur:06-prev,
	author={Peter B\"urgisser},
	title={Lecture notes for \emph{{K}ombinatorik der {D}arstellungstheorie symmetrischer {G}ruppen} ({C}ombinatorics of the representation theory of symmetric groups)},
	note={Lecture held in 2006 at Paderborn University, unpublished notes.}
}
