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Permutations and successions. (English) Zbl 0339.05004


MSC:

05A05 Permutations, words, matrices
05B15 Orthogonal arrays, Latin squares, Room squares
05A15 Exact enumeration problems, generating functions
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[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
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