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JCT
2007
13 years 6 months ago
2007
We define the notions of successive ranks and generalized Durfee squares for overpartitions. We show how these combinatorial statistics give extensions to overpartitions of combin...
JCT
2007
13 years 6 months ago
2007
A matrix A is said to be partition regular (PR) over a subset S of the positive integers if whenever S is finitely coloured, there exists a vector x, with all elements in the sam...
JCT
2007
13 years 6 months ago
2007
Abstract. We develop linear representation theory for bicircular matroids, a chief example being a matroid associated with forests of a graph, and bicircular lift matroids, a chief...
JCT
2007
13 years 6 months ago
2007
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...
JCT
2007
13 years 6 months ago
2007
We show that the Ehrhart h-vector of an integer Gorenstein polytope with a unimodular triangulation satisfies McMullen’s g-theorem; in particular it is unimodal. This result gen...