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**publisher and metadata sources**).Conventional optical networks are based on SONET rings, but since rings are known to use bandwidth inefficiently, there has been much research into shared mesh protection, which promises significant… Continue Reading

IEEE Workshop on High Performance Switching and…

We study the problem of traffic grooming to reduce the number of transceivers in optical networks. We show that this problem is equivalent to a certain traffic maximization problem. We give an… Continue Reading

The problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand has been studied by several researchers. Here we study the related ring-grooming problem… Continue Reading

Many mathematicians have a dismissive attitude towards paradoxes. This is unfortunate, because many paradoxes are rich in content, having connections with serious mathematical ideas as well as having… Continue Reading

Stanley has studied a symmetric function generalization X_G of the chromatic polynomial of a graph G. The innocent-looking Stanley-Stembridge Poset Chain Conjecture states that the expansion of X_G… Continue Reading

Motivated by a 1993 conjecture of Stanley and Stembridge, Shareshian and Wachs conjectured that the characteristic map takes the dot action of the symmetric group on the cohomology of a regular… Continue Reading

There is a strikingly simple classical formula for the number of lattice paths avoiding the line x=ky when k is a positive integer. We show that the natural generalization of this simple formula… Continue Reading

Rook numbers of complementary boards are related by a reciprocity law. A complicated formula for this law has been known for about fifty years, but recently Gessel and the present author… Continue Reading

A set S of positive integers is avoidable if there exists a partition of the positive integers into two disjoint sets such that no two distinct integers from the same set sum to an element of S. Much… Continue Reading

We give an independent set axiomatization of symplectic matroids, a large and important class of Coxeter matroids. As an application, we construct a new class of examples of symplectic matroids from… Continue Reading