Face Rings of Cycles, Associahedra, and Standard Young Tableaux

An Elementary Method for Computing the Kostka Coefficients

Inversions of Semistandard Young Tableaux

A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau columnstandard. An i-inverted Young tableau is a row-standard tableau with precisely i inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableaux. Inverted Young tableaux that lack repeated entries were introdu...

Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers

An inverted semistandard Young tableau is a row-standard tableau along with a collection of inversion pairs that quantify how far the tableau is from being column semistandard. Such a tableau with precisely k inversion pairs is said to be a k-inverted semistandard Young tableau. Building upon earlier work by Fresse and the author, this paper develops generating functions for the numbers of kinv...

Alternating Permutations with Restrictions and Standard Young Tableaux

Abstract. In this paper, we establish bijections between the set of 4123-avoiding In this paper, we establish bijections between the set of 4123-avoiding down-up alternating permutations of length 2n and the set of standard Young tableaux of shape (n, n, n), and between the set of 4123-avoiding down-up alternating permutations of length 2n−1 and the set of shifted standard Young tableaux of sha...

Graph Properties of Graph Associahedra

A graph associahedron is a simple polytope whose face lattice encodes the nested structure of the connected subgraphs of a given graph. In this paper, we study certain graph properties of the 1-skeleta of graph associahedra, such as their diameter and their Hamiltonicity. Our results extend known results for the classical associahedra (path associahedra) and permutahedra (complete graph associa...