Inner tableau translation property of the weak order and related results

Taşkin, Müge

doi:10.1090/S0002-9939-2012-11415-7

Inner tableau translation property of the weak order and related results
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Proc. Amer. Math. Soc. 141 (2013), 837-856 Request permission

Abstract:

Let $SYT_{n}$ be the set of all standard Young tableaux with $n$ cells and $\leq _{weak}$ be Melnikov’s weak order on $SYT_n$. The aim of this paper is to introduce a conjecture on the weak order, named the inner tableau translation property. We prove the conjecture for some special cases and discuss its significance.

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