In this article, we shall start with a closed walk on regular tree of degree d. These walks are described by the Kesten–McKay law which arises as asymptotic distribution random d-regular graph n vertices. We will show that moments given counting standard Young tableaux at most two rows, and how some properties make sense even when d is not an integer. use free probability to instruct us about b...

We elaborate upon a bijection discovered by Cools et al. in [CDPR10] between, on the one hand, rectangular standard Young tableaux, and, on the other hand, representatives, known as G-parking functions, of chip configurations on certain graphs modulo the chip-firing equivalence relation. We present an explcit formula for computing the G-parking function associated to a given tableau, and prove ...

We prove strict unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of Sn representations. Résumé. Nous prouvons l’unimodalité stricte des coefficients q-binomiaux ( n k ) q comme des polynômes en q. La preuve est basée sur la combinatoire de certains Tabl...

We show that the subgraph induced in Young’s graph by the set of partitions with an odd number of standard Young tableaux is a binary tree. This tree exhibits self-similarities at all scales, and has a simple recursive description.

We consider two questions ofWilf related to Standard Young Tableaux. We provide a partial answer to one question, and that will lead us to a more general answer to the other question. Our answers are purely combinatorial.

We give a bijection between the symmetric group Sn, and the set of standard Young tableaux of rectangular shape mn, m > n, that have order n under jeu de taquin promotion.

We give a combinatorial description of the invariant factors associated with certain sequences of product of matrices, over a local principal ideal domain, under the action of the symmetric group by place permutation. Lascoux and Schützenberger have defined a permutation on a Young tableau to associate to each Knuth class a right and left key which they have used to give a combinatorial descrip...