Related papers: Minimal orbits of promotion

We prove that the symmetric group $S_n$ has a unique minimal cover $\mathcal{M}$ by maximal nilpotent subgroups, and we obtain an explicit and easily computed formula for the order of $\mathcal{M}$. In addition, we prove that the order of…

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…

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…

In this manuscript we show that two partial orders defined on the set of standard Young tableaux of shape $\alpha$ are equivalent. In fact, we give two proofs for the equivalence of the box order and the dominance order for {tableaux}. Both…

We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of [Sch\"{u}tzenberger '77] for standard Young tableaux. We apply this to give a new combinatorial rule for the K-theory Schubert calculus of…

In this paper, we study tropical-theoretic aspects of the ``rectification algorithm'' on skew Young tableaux. It is shown that the algorithm is interpreted as a time evolution of some tropical integrable system. By using this fact, we…

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…

(Dual-)promotion and (dual-)evacuation are bijections on SYT(\lambda) for any partition \lambda. Let c^r denote the rectangular partition (c,...,c) of height r, and let sc_k (k > 2) denote the staircase partition (k,k-1,...,1). B. Rhoades…

We prove a collection of conjectures of D. White \cite{WComm}, as well as some related conjectures of Abuzzahab-Korson-Li-Meyer \cite{AKLM} and of Reiner and White \cite{ReinerComm}, \cite{WComm}, regarding the cyclic sieving phenomenon of…

In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the $n$-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length $n$. This result not only gives a lattice…

We consider the involutions known as "toggles," which have been used to give simplified proofs of the fundamental properties of the promotion and evacuation maps. We transfer these involutions so that they generate a group $\mathscr P_n$…

We give a embedding of the Lagrangian Grassmannian LG(n) inside an ordinary Grassmannian that is well-behaved with respect to the Wronski map. As a consequence, we obtain an analogue of the Mukhin-Tarasov-Varchenko theorem for LG(n). The…

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 introduce toric promotion as a cyclic analogue of Sch\"utzenberger's promotion operator. Toric promotion acts on the set of labelings of a graph $G$. We discuss connections between toric promotion and previously-studied notions such as…

We present combinatorial bijections and identities between certain skew Young tableaux, Dyck paths, triangulations, and dissections.

We define a new partial order on $SYT_n$, the set of all standard Young tableaux with $n$ cells, by combining the chain order with the notion of horizontal strips. We prove various desirable properties of this new order.

We give various realizations of the adjoint orbits of a semi-simple Lie group and describe their symplectic geometry. We then use these realizations to identify a family of Lagrangean submanifolds of the orbits.

In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…

The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau $T$, a 1-minor of $T$ is a tableau obtained by first deleting any cell of $T$, and then performing jeu de taquin slides to…

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…