We establish the existence of an involution on tabloids that is analogous to Schützenberger’s evacuation map standard Young tableaux. find number its fixed points given by evaluating a certain Green’s polynomial at $$q = -1$$ , and satisfies “domino-like” recurrence relation.

Abstract. We introduce an infinite family of lower triangular matrices Γ(s), where γ (s) n,i counts the standard Young tableaux on n cells, with at most s columns, whose second and third column lengths differ by i. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number τs(n) of tableaux on n cells and...

In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example Standard Young Tableaux, Standard Monomials, Standard Bitableaux. We adopt a point of view that these standard objects are really non-nesting, and we find their non-crossing counterparts.

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 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.