Related papers: Promotion digraphs
Promotion permutations have recently been associated to each rectangular standard Young tableau by Gaetz--Pechenik--Pfannerer--Striker--Swanson. Here we relate promotion permutations to the Robinson--Schensted (RS) correspondence. More…
A key fact about M.-P. Sch\"{u}tzenberger's (1972) promotion operator on rectangular standard Young tableaux is that iterating promotion once per entry recovers the original tableau. For tableaux with strictly increasing rows and columns,…
In our companion paper, we develop a new $SL_4$-web basis. Basis elements are given by certain planar graphs and are constructed so that important algebraic operations can be performed diagrammatically. A guiding principle behind our…
In this work we study Sch\"utzenberger's promotion operator on standard Young tableaux via a corresponding graphical construction known as $m-$diagrams. In particular, we prove that certain internal structures of SYT are preserved under…
Schutzenberger's promotion operator, pro, is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But pro was subsequently shown to have interesting properties when…
We introduce the notion of a generalized oscillating tableau and define a promotion operation on such tableaux that generalizes the classical promotion operation on standard Young tableaux. As our main application, we show that this…
We show that Sch\"utzenberger's promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following work of the third author, we show that this…
We give a new proof of the cyclic sieving phenomena for promotion on rectangular standard tableaux. This uses an action of the cactus groups in the seminormal bases of the irreducible representations of the Hecke algebras.
The first author recently introduced toric promotion, an operator that acts on the labelings of a graph $G$ and serves as a cyclic analogue of Sch\"utzenberger's promotion operator. Toric promotion is defined as the composition of certain…
We define piecewise-linear and birational analogues of the toggle-involutions on order ideals of posets studied by Striker and Williams and use them to define corresponding analogues of rowmotion and promotion that share many of the…
In 2022, Defant and Kravitz introduced extended promotion (denoted $\partial$), a map that acts on the set of labelings of a poset. Extended promotion is a generalization of Sch\"{u}tzenberger's promotion operator, a well-studied map that…
We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small $m$-Schr\"oder paths and give a bijection between the set of increasing rectangular tableaux and small…
We define P-strict labelings for a finite poset P as a generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with a toggle action on B-bounded Q-partitions of an associated poset…
Using Henriques' and Kamnitzer's cactus groups, Sch\"utzenberger's promotion and evacuation operators on standard Young tableaux can be generalised in a very natural way to operators acting on highest weight words in tensor products of…
In 2012, N. Williams and the second author showed that on order ideals of ranked partially ordered sets (posets), rowmotion is conjugate to (and thus has the same orbit structure as) a different toggle group action, which in special cases…
Sch\"{u}tzenberger's promotion operator is an extensively-studied bijection that permutes the linear extensions of a finite poset. We introduce a natural extension $\partial$ of this operator that acts on all labelings of a poset. We prove…
Let $\delta=(\delta_1,\ldots,\delta_n)$ be a string of letters $h$ and $v$. We define a Young tableau to be $\delta$-semistandard if the entries are weakly increasing along rows and columns, and the entries $i$ form a horizontal strip if…
Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations on representations correspond to…
In this paper we introduce and study a class of tableaux which we call permutation tableaux; these tableaux are naturally in bijection with permutations, and they are a distinguished subset of the Le-diagrams of Alex Postnikov. The…
Inspired by recent work on refraction billiards in dynamics, we introduce a notion of refraction for combinatorial billiards. This allows us to define a generalization of toric promotion that we call toric promotion with reflections and…