ALGEBRAIC COMBINATORICS

[1] Assaf, Sami H.; Speyer, David E. Specht modules decompose as alternating sums of restrictions of Schur modules, Proc. Amer. Math. Soc., Volume 148 (2020) no. 3, pp. 1015-1029 | DOI | MR | Zbl

[2] Ballantine, Cristina M.; Orellana, Rosa C. A combinatorial interpretation for the coefficients in the Kronecker product $s_{(n-p,p)}*s_{\lambda }$, Sém. Lothar. Combin., Volume 54A (2005/07), Paper no. Art. B54Af, 29 pages | MR | Zbl

[3] Bowman, Chris; De Visscher, Maud; Enyang, John The lattice permutation condition for Kronecker tableaux (2018) (arXiv preprint, https://arxiv.org/abs/1812.09175) | Zbl

[4] Bowman, Christopher; De Visscher, Maud; Orellana, Rosa The partition algebra and the Kronecker coefficients, Trans. Amer. Math. Soc., Volume 367 (2015) no. 5, pp. 3647-3667 | DOI | MR | Zbl

[5] Briand, Emmanuel; Orellana, Rosa; Rosas, Mercedes Reduced Kronecker coefficients and counter-examples to Mulmuley’s strong saturation conjecture SH, Comput. Complexity, Volume 18 (2009) no. 4, pp. 577-600 (With an appendix by Ketan Mulmuley) | DOI | MR | Zbl

[6] Briand, Emmanuel; Orellana, Rosa; Rosas, Mercedes The stability of the Kronecker product of Schur functions, J. Algebra, Volume 331 (2011), pp. 11-27 | DOI | MR | Zbl

[7] Butler, Philip H.; King, Roger C. The symmetric group: characters, products and plethysms, J. Mathematical Phys., Volume 14 (1973), pp. 1176-1183 | DOI | MR | Zbl

[8] Church, Thomas; Ellenberg, Jordan S.; Farb, Benson FI-modules and stability for representations of symmetric groups, Duke Math. J., Volume 164 (2015) no. 9, pp. 1833-1910 | DOI | MR | Zbl

[9] Church, Thomas; Farb, Benson Representation theory and homological stability, Adv. Math., Volume 245 (2013), pp. 250-314 | DOI | MR | Zbl

[10] Entova Aizenbud, Inna Deligne categories and reduced Kronecker coefficients, J. Algebraic Combin., Volume 44 (2016) no. 2, pp. 345-362 | DOI | MR | Zbl

[11] Frobenius, Georg F. Über die Charaktere der symmetrischen Gruppe, Königliche Akademie der Wissenschaften, 1900 | DOI | MR | Zbl

[12] Garsia, Adriano M.; Remmel, Jeffrey Shuffles of permutations and the Kronecker product, Graphs Combin., Volume 1 (1985) no. 3, pp. 217-263 | DOI | MR | Zbl

[13] Grinberg, Darij; Reiner, Victor Hopf algebras in combinatorics (2014), 282 pages pages (arXiv preprint, https://arxiv.org/abs/1409.8356) | DOI | MR | Zbl

[14] Islami, Arash Symmetric Functions as Characters of Hyperoctahedral Group, Ph. D. Thesis, York University (2020)

[15] King, Roger C. Branching rules for $GL\left(N\right)\supset {\Sigma }_m$ and the evaluation of inner plethysms, J. Mathematical Phys., Volume 15 (1974), pp. 258-267 | DOI | MR

[16] Lascoux, Alain Symmetric functions (2001), 108 pages (http://www.emis.de/journals/SLC/wpapers/s68vortrag/ALCoursSf2.pdf) | DOI | MR

[17] Littlewood, Dudley E. Products and plethysms of characters with orthogonal, symplectic and symmetric groups, Canadian J. Math., Volume 10 (1958), pp. 17-32 | DOI | MR

[18] Macdonald, Ian G. Symmetric functions and Hall polynomials, Oxford Classic Texts in the Physical Sciences, The Clarendon Press, Oxford University Press, New York, 2015, xii+475 pages (With contribution by A. V. Zelevinsky and a foreword by Richard Stanley, Reprint of the 2008 paperback edition [ MR1354144]) | DOI | MR | Zbl

[19] Murnaghan, Francis D. The characters of the symmetric group, Amer. J. Math., Volume 59 (1937) no. 4, pp. 739-753 | DOI | MR

[20] Murnaghan, Francis D. The analysis of the Kronecker product of irreducible representations of the symmetric group, Amer. J. Math., Volume 60 (1938) no. 3, pp. 761-784 | DOI | MR

[21] Murnaghan, Francis D. On the analysis of the Kronecker product of irreducible representations of $S_n$, Proc. Nat. Acad. Sci. U.S.A., Volume 41 (1955), pp. 515-518 | DOI | MR | Zbl

[22] Nishiyama, Kyo Restriction of the irreducible representations of $G{L}_n$ to the symmetric group $S_n$ (2000), 5 pages (homepage preprint 2021-02-01, http://rtweb.math.kyoto-u.ac.jp/home_kyo/preprint/glntosn.pdf) | DOI | MR

[23] Orellana, Rosa; Zabrocki, Mike Characters of the symmetric group as symmetric functions (2016), 31 pages (arXiv preprint, https://arxiv.org/abs/1605.06672)

[24] Orellana, Rosa; Zabrocki, Mike Products of symmetric group characters, J. Combin. Theory Ser. A, Volume 165 (2019), pp. 299-324 | DOI | MR

[25] Sagan, Bruce E. The symmetric group: representations, combinatorial algorithms, and symmetric functions, 203, Springer Science & Business Media, 2013 | DOI | MR | Zbl

[26] Sage-Combinat community Sage-Combinat: enhancing Sage as a toolbox for computer exploration in algebraic combinatorics, 2008 http://combinat.sagemath.org

[27] Scharf, Thomas; Thibon, Jean-Yves A Hopf-algebra approach to inner plethysm, Advances in Mathematics, Volume 104 (1994) no. 1, pp. 30-58

[28] Scharf, Thomas; Thibon, Jean-Yves; Wybourne, Brian G Generating functions for stable branching coefficients $U\left(n\right)\downarrow S_n$, $O\left(n\right)\downarrow S_n$ and $O(n-1)\downarrow S_n$, J. Phys. A, Volume 30 (1997) no. 19, pp. 6963-6975 | DOI | MR | Zbl

[29] Specht, Wilhelm Die charaktere der symmetrischen gruppe, Math. Z., Volume 73 (1960), pp. 312-329 | DOI | MR | Zbl

[30] Stanley, Richard P. Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, 62, Cambridge University Press, Cambridge, 1999, xii+581 pages | DOI | MR | Zbl

[31] Stein, William; Joyner, David Sage: System for algebra and geometry experimentation, Acm Sigsam Bulletin, Volume 39 (2005) no. 2, pp. 61-64 | DOI | MR | Zbl

[32] Sweedler, Moss E. Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969, vii+336 pages | DOI | MR | Zbl

[33] Young, Alfred The collected papers of Alfred Young (1873–1940), Mathematical Expositions, University of Toronto Press, Toronto, Ont., Buffalo, N. Y., 1977 no. 21, xxvii+684 pages | MR | Zbl