Carlitz, Leonard; Scoville, Richard Enumeration of up-down permutations by upper records. (English) Zbl 0315.05004 Monatsh. Math. 79, 3-12 (1975). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 Documents MSC: 05A15 Exact enumeration problems, generating functions 05B15 Orthogonal arrays, Latin squares, Room squares 05A10 Factorials, binomial coefficients, combinatorial functions PDFBibTeX XMLCite \textit{L. Carlitz} and \textit{R. Scoville}, Monatsh. Math. 79, 3--12 (1975; Zbl 0315.05004) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Triangle read by rows: T(n,k) is the number of down-up permutations on [n] with k left-to-right maxima. References: [1] Carlitz, L., andR. Scoville: Generalized Eulerian numbers; combinatorial applications. J. reine angew. Math.265, 110-137 (1974). · Zbl 0276.05006 [2] Netto, E.: Lehrbuch der Combinatorik. Leipzig und Berlin: Teubner. 1927. · JFM 53.0073.09 [3] Nörlund, N. E.: Vorlesungen über Differenzenrechnung. Berlin: Springer. 1924. · JFM 50.0315.02 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.