Related papers: Minimal orbits of promotion
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…
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…
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 tableaux of two rows and also Dyck paths. We generalize this to a…
Promotion has been well-studied for rectangular standard Young tableaux, in which case the orbit lengths divide the total number of boxes and are described by a cyclic sieving phenomenon (CSP), but little is known about the orbit lengths…
We present an elegant bijection between standard Young tableaux with 2n cells and at most two rows, and pairs of standard Young tableaux of the same shape, with n+1 cells, where only the top row can have more than one cell.
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.
We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we…
We give a new cyclic sieving phenomenon for semistandard Young tableaux $SSYT(\lambda,\mu)$ of shape $\lambda=(m,n^b)$ and content $\mu$, a $(b+2)$-tuple. We prove that $(SSYT(\lambda,\mu),\langle \partial^{b+2} \rangle, f(q))$ exhibits the…
Work of Gaetz, Pechenik, Pfannerer, Striker, and Swanson (2024) introduced promotion permutations for a rectangular standard Young tableau $T$. These promotion permutations encode important features of $T$ and its orbit under…
We consider two partial orders on standard Young tableaux. The first one is induced from the weak right Bruhat order on symmetric group by Robinson-Schensted algorithm. The second one is induced from the order on Young diagrams by…
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…
We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as…
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…
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…
We present a bijection between the set of standard Young tableaux of staircase minus rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted shape. Numerically, this result is due to DeWitt (2012).…
We provide a new branching rule from the general linear group $GL_{2n}(\mathbb{C})$ to the symplectic group $Sp_{2n}(\mathbb{C})$ by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a…
The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin…
For their bijective proof of the hook-length formula for the number of standard tableaux of a fixed shape Novelli, Pak and Stoyanovskii define a modified jeu de taquin which transforms an arbitrary filling of the Ferrers diagram with…
We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is…
Let SYT_n be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYT_n and some of their crucial properties, we prove three main results:…