Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T08:51:10.750Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Berman, G. and Fryer, K. D. (1972), Introduction to combinatorics (Academic Press, New York), 70–72.Google Scholar
Kaplansky, I. and Riordan, J. (1946), ‘The problème des ménages’, Scripta Math. 12, 113–124.Google Scholar
Metropolis, N., Stein, M. L. and Stein, P.R. (1969), ‘Permanents of cyclic (0,1) matrices’, J. Combinatorial Theory 7, 291–321.CrossRefGoogle Scholar
Minc, H. (1964). ‘Permanents of (0, 1) circulants’, Canad. Math. Bull. 7, 253–263.CrossRefGoogle Scholar
Moser, W. O. J. (1967), ‘The number of very reduced 4 x n Latin rectangles’, Canad. J. Math. 19, 1011–1017.Google Scholar
Riordan, J. (1954), ‘Discordant permutations’, Scripta Math. 20, 14–23.Google Scholar
Riordan, J. (1958), Introduction to combinatorial analysis (Wiley, New York), 178–180.Google Scholar
Touchard, J. (1953), ‘Permutations discordant with two given permutations’, Scripta Math. 19, 109–119.Google Scholar
Yamamoto, K. (1956), ‘Structure polynomial of Latin rectangles and its application to a combinatorial problem’, Mem. Fac. Sci. Kyusyu Univ. 10 (Series A), 1–13.Google Scholar