Congruences via Abelian groups

DOI10.1016/0022-314X(85)90041-1zbMath0577.10003MaRDI QIDQ1065843

Bruce E. Sagan

Publication date: 1985

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

symmetric groupscongruencesgroup actionsStirling numbersBell numbersmultinomial coefficientsbinomial coefficientsnumbers of involutionsderangementsnumbers of preferential arrangements

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Other combinatorial number theory (11B75) Congruences; primitive roots; residue systems (11A07) Enumerative combinatorics (05A99) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Permutation groups (20B99)

Related Items

Supercongruences for the Almkvist–Zudilin numbers, A Lucas-type congruence for \(q\)-Delannoy numbers, Congruences derived from group action, Congruence properties of \(q\)-analogs, Combinatorial congruences from \(p\)-subgroups of the symmetric group, Congruences for Catalan and Motzkin numbers and related sequences, A \(q\)-analogue of Wilson's congruence

Cites Work

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• Some congruences for the Bell polynomials
• Congruences derived from group action
• From sets to functions: Three elementary examples
• Generalized Kummer congruences for the products of sequences. Applications
• The iterated exponential integers
• Congruences for generalized Bell and Stirling numbers
• Nombres Exponentiels Et Nombres De Bernoulli
• Preferential Arrangements
• Some Properties of Generalized Euler Numbers
• Some Congruences for Generalized Euler Numbers
• Notes on Binomial Coefficients I-A Generalization of Lucas' Congruence†
• Notes on Binomial Coefficients Ii-The Least N such that p^e Divides an r -Nomial Coefficient of Rank n †
• Notes on Binomial Coefficients Iii-Any Integer Divides Almost All Binomial Coefficients†
• Arithmetic properties of Bell numbers to a composite modulus I
• On a Transformation of Bilateral Series with Applications
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Generalized Stirling Transforms of Sequences
• The Arithmetic of Bell and Stirling Numbers
• On Recursions Connected With Symmetric Groups I
• On Solutions of x^d = 1 In Symmetric Groups