EJC
2011
12 years 8 months ago
2011
Answering a question of B´ona, it is shown that for n ≥ 2 the probability that 1 and 2 are in the same cycle of a product of two n-cycles on the set {1, 2, . . . , n} is 1/2 if...
EJC
2011
12 years 8 months ago
2011
We provide a new proof of Brylawski’s formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte’s formula, expressing the Tutte...
EJC
2011
12 years 11 months ago
2011
Abstract. We introduce a new axiomatization of oriented matroids that requires the elimination property only among modular pairs of circuits. This new point of view leads also to a...
EJC
2011
12 years 11 months ago
2011
Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. The Frobenius number of this N-tuple is defined to be the largest positive integer that has no re...
EJC
2011
12 years 11 months ago
2011
Henning and Yeo proved a lower bound for the minimum size of a maximum matching in a connected k-regular graphs with n vertices; it is sharp infinitely often. In an earlier paper...
EJC
2011
12 years 11 months ago
2011
Noncrossing set partitions, nonnesting set partitions, Dyck paths, and rooted plane trees are four classes of Catalan objects which carry a notion of type. There exists a product f...
EJC
2011
12 years 11 months ago
2011
A D-polyhedron is a polyhedron P such that if x, y are in P then so are their componentwise max and min. In other words, the point set of a D-polyhedron forms a distributive latti...
EJC
2011
12 years 11 months ago
2011
EJC
2011
12 years 11 months ago
2011
We present an algorithm which takes a graph as input and decides in cubic time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algor...