Increasing Subsequences and Kronecker Coefficients

Abstract

It has been conjectured by W. Chen that the distribution of the length of the longest increasing subsequence in a uniformly random permutation is log-concave. We propose a stronger version of this conjecture which involves the Kronecker coefficients of the symmetric group.

5 pages, for the "Open Problems in Algebraic Combinatorics" AMS volume to accompany the OPAC 2021 conference at the University of Minnesota

References in corpus (3)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Log-concavity and q-Log-convexity Conjectures on the Longest Increasing Subsequences of Permutations
• Lefschetz theory for exterior algebras and fermionic diagonal coinvariants