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Four-discordant permutations

Part of: Combinatorics

Published online by Cambridge University Press:  09 April 2009

Earl Glen Whitehead Jr
Earl Glen Whitehead Jr
Affiliation:
Department of Mathematics and Statistics University of PittsburghPittsburgh, PA 15260, U.S.A.
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Abstract

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A permutation π of the set {1, 2, …, n} is four-discordant if π(i) ≢ i, i+ 1, i + 2, i +3 (mod n) for 1 ≦i ≦ n. Generating functions for rook polynomials associated with four-discordant permutations are derived. Hit polynomials associated with four-discordant permutations are studied. Finally, it is shown that the leading coefficients of these rook polynomials form a “tribonacci” sequence which is a generalized Fibonacci sequence.

MSC classification

Secondary: 05A05: Permutations, words, matrices 05A15: Exact enumeration problems, generating functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 369 - 377
Copyright
Copyright © Australian Mathematical Society 1979

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