Keys and alternating sign matrices

Abstract

Lascoux and Schützenberger introduced a notion of key associated to any Young tableau. More recently Lascoux defined the key of an alternating sign matrix by recursively removing all -1's in such matrices. But alternating sign matrices are in bijection with monotone triangles, which form a subclass of Young tableaux. We show that in this case these two notions of keys coincide. Moreover we obtain an elegant and direct way to compute the key of any Young tableau, and discuss consequences of our result.

References in corpus (5)

• Another proof of the alternating sign matrix conjecture
• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Combinatorial nature of ground state vector of O(1) loop model
• An Explicit Construction of Type A Demazure Atoms

Cited by in corpus (7)

• Diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Multiply-refined enumeration of alternating sign matrices
• Notes on Schubert, Grothendieck and Key Polynomials
• Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
• Row-strict Quasisymmetric Schur Functions, Characterizations of Demazure Atoms, and Permuted Basement Nonsymmetric Macdonald Polynomials
• Colored five-vertex models and Demazure atoms
• Sign-restricted matrices of $0$'s, $1$'s, and $-1$'s