Tanny, Stephen M. Permutations and successions. (English) Zbl 0339.05004 J. Comb. Theory, Ser. A 21, 196-202 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 18 Documents MSC: 05A05 Permutations, words, matrices 05B15 Orthogonal arrays, Latin squares, Room squares 05A15 Exact enumeration problems, generating functions PDFBibTeX XMLCite \textit{S. M. Tanny}, J. Comb. Theory, Ser. A 21, 196--202 (1976; Zbl 0339.05004) Full Text: DOI Online Encyclopedia of Integer Sequences: Rencontres numbers: number of permutations of [n] with exactly one fixed point. Triangle read by rows: T(n,k) is the number of permutations of [n] with k circular successions (0<=k<=n-1). A circular succession in a permutation p of [n] is either a pair p(i), p(i+1), where p(i+1)=p(i)+1 or the pair p(n), p(1) if p(1)=p(n)+1. Number of permutations of [n] having exactly 1 circular succession. A circular succession in a permutation p of [n] is either a pair p(i), p(i+1), where p(i+1)=p(i)+1 or the pair p(n), p(1) if p(1)=p(n)+1. References: [1] Abramson, M.; Moser, W., Combinations, successions and the \(n\)-kings problem, Math. Mag., 39, 269-273 (1966) · Zbl 0146.01203 [2] Dwass, M., The number of increases in a random permutation, J. Combinatorial Theory A, 15, 192-199 (1973) · Zbl 0296.60009 [3] Kaplansky, I., Symbolic solutions of certain problems in permutations, Bull. Amer. Math. Soc., 50, 906-914 (1944) · Zbl 0063.03136 [4] Kaplansky, I., The asymptotic distribution of runs of consecutive elements, Ann. Math. Statist., 16, 200-203 (1945) · Zbl 0063.03137 [5] Riordan, J., A recurrence for permutations without rising or falling successions, Ann. Math. Statist., 36, 745-748 (1965) [6] Riordan, J., An Introduction to Combinatorial Analysis (1958), Wiley: Wiley New York · Zbl 0078.00805 [7] Roselle, D. P., Permutations by number of rises and successions, (Proc. Amer. Math. Soc., 19 (1968)), 8-16 · Zbl 0159.30101 [8] Tietze, H., Über gewisse Unordnungen von Permutationen, S.-B. Math.-Natur. Abt. Bayer. Akad. Wiss., 281-293 (1943) [9] Whitworth, W. A., Choice and Chance (1943), Stechert: Stechert New York · JFM 11.0163.02 [10] Paige, L. J.; Swift, J. D., Elements of Linear Algebra (1961), Blaisdell: Blaisdell New York · Zbl 0093.24101 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.