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Kostka, Littlewood-Richardson, Kronecker, and plethysm coefficients are fundamental quantities in algebraic combinatorics, yet many natural questions about them stay unanswered for more than 80 years.
F. D. Murnaghan, The analysis of the Kronecker product of irreducible representations of the symmetric group, Amer. J. Math. 60
1938
Earlier work this paper cites.
J. S. Frame, G. de B. Robinson and R. M. Thrall, The hook graphs of the symmetric group, Canad. J. Math
1954
Earlier work this paper cites.
F. D. Murnaghan, On the Kronecker product of irreducible representations of the symmetric group, Proc. Natl. Acad. Sci. USA 42
1956
Earlier work this paper cites.
C. Ikenmeyer, The Saxl conjecture and the dominance order, Disc. Math. (11) 6
1975
Earlier work this paper cites.
B. F. Logan and L. A. Shepp, A variational problem for random Young tableaux, Adv. Math. 26
1977
Earlier work this paper cites.
M. R. Garey and D. S. Johnson, Computers and intractability , Freeman, San Francisco, CA, 1979
1979
Earlier work this paper cites.
A. Lascoux, Produit de Kronecker des représentations du groupe symétrique. Séminaire dÀlgèbre Paul Dubreil et Marie-Paule Malliavin: Proceedings , Paris 1979 (32ème Année), pages 319–329 (1979)
1979
Earlier work this paper cites.
L. G. Valiant, Completeness classes in algebra. Proc. 11th STOC (1979), 249–261
1979
Earlier work this paper cites.
L. G. Valiant, The complexity of computing the permanent. Theor. Comp. Sci. 8
1979
Earlier work this paper cites.
A. M. Garsia and J. Remmel, Shuffles of permutations and the Kronecker product, Graphs and Combinatorics (1985), 1:217-263
1985
Earlier work this paper cites.
A. M. Vershik and S. V. Kerov, Asymptotic of the largest and the typical dimensions of irreducible representations of a symmetric group, Funct. Anal. Appl. 19
1985
Earlier work this paper cites.
M. Brion, Stable properties of plethysm: on two conjectures of Foulkes, Manuscripta mathematica (1993), 80
1993
Earlier work this paper cites.
Y. Dvir, On the Kronecker product of S n S_{n} characters, J. Algebra 154
1993
Earlier work this paper cites.
J. Remmel, T. Whitehead, On the Kronecker product of Schur functions of two row shapes. Bull. Belg. Math. Soc. Simon Stevin 1
1994
Earlier work this paper cites.
I. G. Macdonald, Symmetric functions and Hall polynomials (Second edition), Oxford University Press, New York, 1995
1995
Earlier work this paper cites.
P. Bürgisser, M. Clausen and M. A. Shokrollahi, Algebraic complexity theory , Springer, Berlin, 1997
1997
Earlier work this paper cites.
W. Fulton, Young tableaux , Cambridge Univ. Press, Cambridge, UK, 1997, 260 pp
1997
Earlier work this paper cites.
E. Vallejo, Reductions of additive sets, sets of uniqueness and pyramids, Discrete Math. 173
1997
Earlier work this paper cites.
Ph. Biane, Representations of Symmetric Groups and Free Probability, Adv. Math. 138
1998
Earlier work this paper cites.
A. Knutson and T. Tao, The honeycomb model of GL n ( ℂ ) \mathrm{GL}_{n}(\mathbb{C}) tensor products I: Proof of the saturation conjecture, J. AMS
1999
Earlier work this paper cites.
R. P. Stanley, Enumerative Combinatorics
1999
Earlier work this paper cites.
E. Vallejo, Stability of Kronecker products of irreducible characters of the symmetric group, Electron. J. Combin. 6
1999
Earlier work this paper cites.
P. Bürgisser, Completeness and reduction in algebraic complexity theory , Springer, Berlin, 2000, 168 pp
2000
Earlier work this paper cites.
P. Bürgisser, Cook’s versus Valiant’s hypothesis, Theor. Comp. Sci. 235
2000
Earlier work this paper cites.
W. Fulton, Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. AMS 37
2000
Earlier work this paper cites.
R. P. Stanley, Positivity problems and conjectures in algebraic combinatorics, in Mathematics: frontiers and perspectivies , AMS, Providence, RI, 2000, 295–319
2000
Earlier work this paper cites.
K. D. Mulmuley and M. Sohoni, Geometric complexity theory. I An approach to the P
2001
Earlier work this paper cites.
B. E. Sagan, The symmetric group (Second ed.), Springer, New York, 2001
2001
Earlier work this paper cites.
C. Bessenrodt and C. Behns, On the Durfee size of Kronecker products of characters of the symmetric group and its double covers, J. Algebra
2004
Earlier work this paper cites.
A. N. Kirillov, An invitation to the generalized saturation conjecture, Publ. RIMS 40
2004
Earlier work this paper cites.
C. Ballantine, R. Orellana, A combinatorial interpretation for the coefficients in the Kronecker product s ( n − p , p ) ∗ s λ s_{(n-p,p)}*s_{\lambda} . Sém. Lothar. Combin. 54A
2005
Cited alongside, same era.
F. Bergeron, R. Biagioli and M. H. Rosas, Inequalities between Littlewood–Richardson coefficients, J. Combin. Theory, Ser. A 113
2006
Cited alongside, same era.
J. A. De Loera and T. B. McAllister, On the computation of Clebsch–Gordan coefficients and the dilation effect, Experimental Math. 15
2006
Cited alongside, same era.
H. Narayanan, On the complexity of computing Kostka numbers and Littlewood–Richardson coefficients, J. Algebraic Combin. 24
2006
Cited alongside, same era.
M. Christandl, A. Harrow, G. Mitchison, Nonzero Kronecker coefficients and what they tell us about spectra. Comm. Math. Phys. 270
2007
Cited alongside, same era.
F. Gesmundo, C. Ikenmeyer and G. Panova, Geometric complexity theory and matrix powering, Diff. Geom. Applications 55
2017
Later among the works it cites.
C. Ikenmeyer, K. D. Mulmuley and M. Walter, On vanishing of Kronecker coefficients, Computational Complexity 26
2017
Later among the works it cites.
Ricky Liu, A simplified Kronecker rule for one hook shape, Proc. Amer. Math. Soc. (2017), 145
2017
Later among the works it cites.
S. Luo,M. Sellke, The Saxl conjecture for fourth powers via the semigroup property. J. Algebraic Combin. 45
2017
Later among the works it cites.
K. Mulmuley, Geometric Complexity Theory V. Efficient algorithms for Noether normalization, J. AMS 30
2017
Later among the works it cites.
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P. Bürgisser, C. Ikenmeyer, The complexity of computing Kronecker coefficients. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), pp. 357–368
2008
Cited alongside, same era.
K. D. Mulmuley and M. Sohoni, Geometric complexity theory. II Towards explicit obstructions for embeddings among class varieties, SIAM J. Comput
2008
Cited alongside, same era.
E. Briand, R. Orellana and M. Rosas, The stability of the Kronecker product of Schur functions, J. Algebra 331
2011
Cited alongside, same era.
P. Bürgisser, J. M. Landsberg, L. Manivel and J. Weyman, An overview of mathematical issues arising in the Geometric Complexity Theory approach to VP = ? VNP {{\rm{\textsf{VP}}}}\overset{?}{=}{{\rm{\textsf{VNP}}}} , SIAM J. Comput. 40
2011
Cited alongside, same era.
2011
Cited alongside, same era.
M. Christandl, B. Doran and M. Walter, Computing Multiplicities of Lie Group Representations, in Proc. 53-rd FOCS (2012), IEEE, 639–648
2012
Cited alongside, same era.
K. D. Mulmuley, H. Narayanan and M. Sohoni, Geometric complexity theory III. On deciding nonvanishing of a Littlewood-Richardson coefficient, J. Algebraic Combin. 36
2012
Cited alongside, same era.
2017
Later among the works it cites.
I. Pak and G. Panova, On the complexity of computing Kronecker coefficients, Comput. Complexity 26
2017
Later among the works it cites.
C. Bessenrodt, Critical classes, Kronecker products of spin characters, and the Saxl conjecture, Alg. Combinatorics 1
2018
Later among the works it cites.
J. Blasiak, R.I. Liu, Kronecker coefficients and noncommutative super Schur functions. J. Combin. Theory Ser. A 158
2018
Later among the works it cites.
M. Bläser and C. Ikenmeyer, Introduction to geometric complexity theory , Summer school lecture notes, 2018, 148 pp.; https://tinyurl.com/nhe2wxvw
2018
Later among the works it cites.
J. Dörfler, C. Ikenmeyer and G. Panova, On geometric complexity theory: Multiplicity obstructions are stronger than occurrence obstructions in Proc. 46-th ICALP (2019), Art. 51, 14 pp. i
2019
Later among the works it cites.
S. Melczer, G. Panova and R. Pemantle, Counting partitions inside a rectangle, SIAM J. Discrete Math. 34
2019
Later among the works it cites.
I. Pak, G. Panova and D. Yeliussizov, On the largest Kronecker and Littlewood–Richardson coefficients, J. Combin. Theory, Ser. A 165
2019
Later among the works it cites.
A. Wigderson, Mathematics and Computation , monograph draft, 2019
2019
Later among the works it cites.
N. Fischer and C. Ikenmeyer, The computational complexity of plethysm coefficients, Comput. Complexity 29
2020
Later among the works it cites.
R. Orellana, M. Zabrocki, A combinatorial model for the decomposition of multivariate polynomials rings as an S n S_{n} -module The Elect. Journal of Comb. 27
2020
Later among the works it cites.
I. Pak and G. Panova, Bounds on Kronecker coefficients via contingency tables, Linear Alg. Appl. 602
2020
Later among the works it cites.
C. Bessenrodt, C. Bowman, L. Sutton, Kronecker positivity and 2-modular representation theory, Trans. Amer. Math. Soc. Ser. B 8
2021
Later among the works it cites.
Xin Li, Saxl Conjecture for triple hooks, Discrete Math. 344
2021
Later among the works it cites.
M. Mishna, M. Rosas, S. Sundaram, Vector partition functions and Kronecker coefficients, J. Phys. A: Math. Theor. (2021) 54
2021
Later among the works it cites.
R. Orellana, M. Zabrocki, Symmetric group characters as symmetric functions Adv. Math. 390
2021
Later among the works it cites.
S. Belinschi, A. Guionnet, J. Huang, Large deviation principles via spherical integrals, Prob. Math. Phys. 3
2022
Later among the works it cites.
2022
Later among the works it cites.
C. Ikenmeyer and I. Pak, What is in #P
2022
Later among the works it cites.
R. Orellana, F. Saliola, A. Schilling, M. Zabrocki, Plethysm and the algebra of uniform block permutations, Alg. Combinatorics 5
2022
Later among the works it cites.
I. Pak, What is a combinatorial interpretation?, preprint (2022), 58 pp.; to appear in Proc. OPAC , AMS, Providence, RI
2022
Later among the works it cites.
2023
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C. Ikenemeyer and G. Panova, All Kronecker coefficients are reduced Kronecker coefficients, (2023)
2023
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I. Pak, G. Panova, Durfee squares, symmetric partitions and bounds on Kronecker coefficients, J. Algebra (2023), to appear
2023
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G. Panova, Computational Complexity in Algebraic Combinatorics, Current Developments in Mathematics , Harvard University (2023)
2023
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