Foulkes, H. O. Eulerian numbers, Newcomb’s problem and representations of symmetric groups. (English) Zbl 0445.05008 Discrete Math. 30, 3-49 (1980). Reviewer: Guy Henniart (Paris) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 17 Documents MSC: 05A15 Exact enumeration problems, generating functions 05A17 Combinatorial aspects of partitions of integers 20C30 Representations of finite symmetric groups 11B68 Bernoulli and Euler numbers and polynomials Keywords:enumeration theory; Euler numbers; Stirling numbers; Newcomb’s problem; representations of symmetric groups; skew hooks; Kostka numbers PDF BibTeX XML Cite \textit{H. O. Foulkes}, Discrete Math. 30, 3--49 (1980; Zbl 0445.05008) Full Text: DOI References: [1] Abramson, M., A simple solution of Simon Newcomb’s problem, J. combinatorial theory (A), 18, 223-225, (1975) · Zbl 0305.05006 [2] Barton, D.E.; Mallows, C.L., Some aspects of the random sequence, Ann. math. statist., 36, 236-260, (1965) · Zbl 0128.13001 [3] Carlitz, L., Enumeration of sequences by rises and falls; a refinement of the Simon newcomb problem, Duke math. J., 39, 267-280, (1972) · Zbl 0243.05008 [4] Comtet, L., Advanced combinatorics, (1974), Reidel Boston [5] Dillon, J.F.; Roselle, D.P., Simon Newcomb’s problem, SIAM J. applied math., 17, 1086-1093, (1969) · Zbl 0212.34701 [6] Foata, D., La série génératrice exponentielle dans LES problèmes d’énumération, () · Zbl 0325.05007 [7] Foata, D., Studies in enumeration, () [8] Foata, D.; Schützenberger, M.P., Théorie Géométrique des polynômes eulériens, () · Zbl 0214.26202 [9] Foulkes, H.O., Differential operators associated with S-functions, J. lond. math. soc., 24, 136-143, (1949) · Zbl 0037.00902 [10] Foulkes, H.O., Paths in ordered structures of partitions, Discrete math., 9, 365-374, (1974) · Zbl 0303.05011 [11] Foulkes, H.O., Enumeration of permutations with prescribed up-down and inversion sequences, Discrete math., 15, 235-252, (1976) · Zbl 0338.05002 [12] Foulkes, H.O., Tangent and secant numbers and representations of symmetric groups, Discrete math., 15, 311-324, (1976) · Zbl 0342.20005 [13] Foulkes, H.O., A non-recursive combinatorial rule for Eulerian numbers, J. combinatorial theory, ser. A, 22, 245-248, (1977) · Zbl 0351.05009 [14] Grosner, E., A characterization of permutations via skew-hooks, J. combinatorial theory, ser. A, 23, 176-179, (1977) · Zbl 0363.05014 [15] Kostka, C., Über den zusammenhang zwischen einigen formen von symmetrischen functionen, J. reine angew. math., 93, 89-123, (1882) · JFM 14.0112.02 [16] Kostka, C., Tafeln für symmetrische funktionen bis zur elften dimension, mit kurzen erläuterungen, Sch. progr., (1908), (Insterburg) · JFM 39.0222.01 [17] Kreweras, G., Traitement simultané du problème de Young et du problème de Simon newcomb, Cahiers bur. univ. recherche opér, 10, 23-31, (1967), (Paris) [18] Littlewood, D.E., The theory of group characters and matrix representations of groups, (1950), Oxford University Press Oxford · Zbl 0038.16504 [19] MacMahon, P.A., Combinatory analysis, Vol. 1, (1915), Cambridge University Press Cambridge · JFM 45.1271.01 [20] Riordan, J., An introduction to combinatorial analysis, (1958), Wiley New York · Zbl 0078.00805 [21] Solomon, L., A decomposition of the group algebra of a finite Coxeter group, J. algebra, 9, 220-239, (1968) · Zbl 0186.04503 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.