WebSep 5, 2014 · Starting with Schur-Weyl duality, we explain how polynomials can be written down as symmetrizations of highest weight vectors in a tensor power of C^n. Studying these polynomials leads to interesting questions in combinatorics, for example a famous conjecture about Latin Squares by Alon and Tarsi. Our goal is to explain the results of … WebNov 4, 2024 · In two papers, Bürgisser and Ikenmeyer (STOC 2011, STOC 2013) used an adaption of the geometric complexity theory (GCT) approach by Mulmuley and Sohoni (Siam J Comput 2001, 2008) to prove lower bounds on the border rank of the matrix multiplication tensor. A key ingredient was information about certain Kronecker coefficients. While …
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WebAnkit Garg, Christian Ikenmeyer, Visu Makam, Rafael Mendes de Oliveira, Michael Walter, Avi Wigderson: Search Problems in Algebraic Complexity, GCT, and Hardness of … WebJul 27, 2024 · Christian Ikenmeyer & Greta Panova (2016). Rectangular Kronecker coefficients and plethysms in geometric complexity theory. In Proceedings of the 57th FOCS, 396–405. IEEE. Kadish H., Landsberg J. (2014) Padded polynomials, their cousins, and geometric complexity theory. Communications in Algebra 42(5): 2171–2180 cork board message center
The Computational Complexity of Plethysm Coefficients
WebAug 1, 2016 · Christian Ikenmeyer; Igor Pak; For several classical nonnegative integer functions, we investigate if they are members of the counting complexity class #P or not. We prove #P membership in ... WebChristian Ikenmeyer 12. Kronecker coe cients Theorem (Mulmuley and Sohoni) If the rectangular Kronecker coe cient g( ;d;m) is zero, then all highest weight vectors of type vanish on Vm(n). Studied since the 1950s, many papers that treat special cases, but mostly not understood. WebSep 29, 2024 · Peter Bürgisser, Matthias Christandl, and Christian Ikenmeyer. Even partitions in plethysms. Journal of Algebra, 328(1):322--329, 2011. Google Scholar Cross Ref; Peter Bürgisser and Christian Ikenmeyer. Geometric complexity theory and tensor rank. Proceedings 43rd Annual ACM Symposium on Theory of Computing 2011, pages … f and p shared reading