Permutations and sequences

DOI10.1016/0001-8708(74)90025-5zbMath0285.05011OpenAlexW2083050195MaRDI QIDQ1844839

Leonard Carlitz

Publication date: 1974

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(74)90025-5

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items (10)

Some stochastic processes in a random permutation ⋮ On the distribution of the number of occurrences of an order-preserving pattern of length three in a random permutation ⋮ The Dumont ansatz for the Eulerian polynomials, peak polynomials and derivative polynomials ⋮ Binomial posets, Möbius inversion, and permutation enumeration ⋮ Subalgebras of Solomon's descent algebra based on alternating runs ⋮ A Formal Calculus for the Enumerative System of Sequences-I. Combinatorial Theorems ⋮ A Formal Calculus for the Enumerative System of Sequences-II. Applications ⋮ A Formal Calculus for the Enumerative System of Sequences-III. Further Developments ⋮ On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations ⋮ On zigzag permutations and comparisons of adjacent elements

Cites Work

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• Extended Bernoulli and Eulerian numbers
• Enumeration of permutations of \((1, \ldots, n)\) by number of maxima
• Sequences and inversions
• Théorie géométrique des polynômes eulériens
• Sequences with adjacent elements unequal
• Enumeration of sequences by rises and falls: a refinement of the Simon Newcomb problem
• Enumeration of up-down sequences
• Up-down sequences
• Simon Newcomb’s Problem
• On the Generating Function for Permutations with Repetitions and Inversions

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