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23 papers · 1 filter
Matching polytopes and Specht modules
Ricky Ini Liu
We prove that the dimension of the Specht module of a forest is the same as the normalized volume of the matching polytope of . We also associate to a symmetric function…
The shifted plactic monoid
Luis Serrano
We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the \emph{shifted plactic monoid}. It can be defined in two different ways: via the \emph{shifted…
Quantized dual graded graphs
Thomas Lam
We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation DU - qUD = rI. We construct examples based upon: the Fibonacci poset,…
Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties
Alan Stapledon
We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of th…
A non-crossing standard monomial theory
T. Kyle Petersen, Pavlo Pylyavskyy, David E Speyer
The second author has introduced non-crossing tableaux, objects whose non-nesting analogues are semi-standard Young tableaux. We relate non-crossing tableaux to Gelfand-Tsetlin pat…
Promotion and cyclic sieving via webs
T. Kyle Petersen, Pavlo Pylyavskyy, Brendon Rhoades
We show that Schützenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreove…