Keys and alternating sign matrices

Details Keys and alternating sign matrices Keys and alternating sign matrices

2007-11-14

arxiv.org/abs/0711.2150v2

Seminaire Lotharingien de Combinatoire 59 (2008) B59f

Mathematics

Combinatorics

Scientific paper

Lascoux and Sch\"utzenberger 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.

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