Barely set-valued tableaux are a variant of Young in which one box contains two numbers as its entry. It has recently been discovered that there product formulas enumerating certain classes barely tableaux. We give some q-analogs these by introducing version major index for also and plane partitions. Many the results stated generality P-partitions then specialize to particularly nice rectangles...

Given a list of vectors that contains directions of the edges of a given polytope P and the availability of an algorithm that solves linear programs over P , we describe a method for enumerating the vertices of P; in particular, the method is adaptable to polytopes which are presented as (linear) projections of polytopes having linear inequality representation. Polynomial complexity bounds unde...

By jagged partitions we refer to an ordered collection of non-negative integers (n 1 , n 2 , · · · , n m) with n m ≥ p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in greater detail here corresponds to p = 1 and the following conditions n i ≥ n i+1 − 1 and n i ≥ n i+2. A number of properties f...