Transactions of the American Mathematical Society, Vol. 332, No. 2 (Aug., 1992), pp. 729-756 (28 pages) In this paper we present several results and open problems about log-concavity properties of ...

We develop the concept of partition categories, in order to extend the Mullin-Rota theory of binomial enumeration, and simultaneously to provide a natural setting for recent applications of the ...

Graph colouring is a fundamental problem in both theoretical and applied combinatorics, with significant implications for computer science, operational research and network theory. At its essence, ...

In a recent article, mathematicians explain the use of tools from the branch of mathematics called graph theory to systematically analyze Sudoku puzzles. They also find that analyzing Sudokus leads to ...

Conjecture 1 (Tutte [2]): If G is a 2-edge-connected graph, then G admits a nowhere-zero 5-flow. If true, Conjecture 1 would imply that for every integer k > 4, the flow polynomial of any ...