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The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q ¼ À1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Poíya–Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite(More)
To Anders Björner on his 60 th birthday. Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and(More)
Let M be a finite matroid with rank function r. We will write A ⊆ M when we mean that A is a subset of the ground set of M , and write M | A and M/A for the matroids obtained by restricting M to A, and contracting M on A respectively. Let M * denote the dual matroid to M. (See [1] for definitions). The main theorem is Theorem 1. The Tutte polynomial T M (x,(More)