We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work
of Schützenberger (1977) for standard Young tableaux. We apply this to give a new …

The irreducible representations of symmetric groups can be realized as certain graded
pieces of invariant rings, equivalently as global sections of line bundles on partial flag …

An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It
is well known that the Catalan numbers enumerate both rectangular standard Young …

The symmetric Grothendieck polynomials representing Schubert classes in the K theory of
Grassmannians are generating functions for semistandard set-valued tableaux. We …

In certain finite posets, the expected down-degree of their elements is the same whether
computed with respect to either the uniform distribution or the distribution weighting an …

We explain how genomic tableaux [Pechenik–Yong'15] are a semistandard complement to
increasing tableaux [Thomas–Yong'09]. From this perspective, one inherits genomic …

We give a Uq (sln)-crystal structure on multiset-valued tableaux, hook-valued tableaux, and
valued-set tableaux, whose generating functions are the weak symmetric, canonical, and …

We define a K-theoretic analogue of Fomin's dual graded graphs, which we call dual filtered
graphs. The key formula in the definition is DU− UD= D+I. Our major examples are K …

Patrias and Pylyavskyy introduced shifted Hecke insertion as an application of their theory of
dual filtered graphs. We study shifted Hecke insertion, showing it preserves descent sets …

This paper considers whether non-trivial identities are satisfied by certainplactic-
like'monoids that, like the plactic monoid, are closely connected to combinatorics. New …