Santmyer, Joseph M. Five discordant permutations. (English) Zbl 0789.05001 Graphs Comb. 9, No. 3, 279-292 (1993). Author’s abstract: A permutation \(\pi\) of \(\{1,2,\dots,n\}\) is 5- discordant if \(\pi(i) \neq i\), \(i+1\), \(i+2\), \(i+3\), \(i+4 \pmod n\) for \(1 \leq i \leq n\). A system of recurrences for computing the rook polynomials associated with 5-discordant permutations is derived. This system, together with hit polynomials enable the 5-discordant permutations to be enumerated. Reviewer: J.Cigler (Wien) Cited in 1 Document MSC: 05A05 Permutations, words, matrices 05A15 Exact enumeration problems, generating functions Keywords:permutation; rook polynomials PDFBibTeX XMLCite \textit{J. M. Santmyer}, Graphs Comb. 9, No. 3, 279--292 (1993; Zbl 0789.05001) Full Text: DOI References: [1] Bogart, K., Introductory combinatorics (1983), Pitman: Marshfield, Pitman · Zbl 0545.05001 [2] Kaplansky, I.; Riordan, J., The problème des ménages, Scripta Math., 12, 113-124 (1953) · Zbl 0060.02905 [3] Metropolis, N.; Stein, M. L.; Stein, P. R., Permanents of cyclic (0,1) matrices, J. Com. Theory, 7, 291-304 (1969) · Zbl 0183.29803 · doi:10.1016/S0021-9800(69)80058-X [4] Riordan, J., Discordant permutations, Scripta Math., 20, 14-23 (1954) · Zbl 0058.25003 [5] Riordan, J., An introduction to combinatorial analysis (1978), New Jersey: Princeton University Press, New Jersey [6] Touchard, J., Sur un probléme permutations, C. R. Acad. Sci. Paris., 198, 631-633 (1934) · JFM 60.0049.02 [7] Whitehead, E. G., Four-discordant permutations, J. Aust. Math. Soc. Ser. A, 28, 369-377 (1979) · Zbl 0429.05003 · doi:10.1017/S1446788700012337 [8] Yamamoto, K., Structure polynomial of latin rectangles and its application to a combinatorial problem, Mem. Fac. Sci. Kyrusyu Univ., 10, 1-13 (1956) · Zbl 0070.01102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.