Franklin [2] gave a wonderful combinatorial proof of this theorem. It is clear that the left side of (1.1) is the generating function for partitions with distinct parts, each part weighted by -1. Ifâ€¦ (More)

Consider the collection of all integer partitions, whose part sizes lie in a given set. Such a set is called monotone if the generating function has weakly increasing coefficients. The monotoneâ€¦ (More)

The purpose of this paper is to study the relationship between the rook vector of a general board and the chromatic structure of an associated set of graphs. Although part of a numbered series, thisâ€¦ (More)

It is well-known that if T is an everywhere defined bounded operator on a Banach space X to a Banach space Y and T* is its adjoint, then the range R(T*) of T* is closed in X* if and only if the rangeâ€¦ (More)