Rook polynomials and counting permutations by cycles

Ira Gessel

Brandeis University

September 8,
refreshments at 3:45pm


The classical theory of rook polynomials gives a way to count permutations p of [n] = {1,2,..., n} according to the number of pairs (i, p(i)) lying in some specified subset of [n] x [n]. I will discuss a generalization in which we keep track of the number of cycles of the permutation. The theory involves a new basis for polynomials and gives some new "twisted" versions of the Eulerian polynomials.

Speaker's Contact Info: gessel(at-sign)

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

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