Enumeration by kernel positions

DOI10.1016/j.aam.2008.11.001zbMath1169.05302OpenAlexW2016196182MaRDI QIDQ1015168

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Publication date: 7 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.aam.2008.11.001

zbMATH Keywords

generating functionsBernoulli polynomialsdigamma functionenumerative combinatoricsdegenerate Bernoulli numbersEuler's \(C\) constantkernel positionNewton expansionprogressively finite games

Mathematics Subject Classification ID

Umbral calculus (05A40) Exact enumeration problems, generating functions (05A15) 2-person games (91A05) Bernoulli and Euler numbers and polynomials (11B68) Combinatorial games (91A46) Probabilistic games; gambling (91A60)

Related Items (7)

ON THE LOG-CONCAVITY OF THE DEGENERATE BERNOULLI NUMBERS ⋮ Counting Domineering Positions ⋮ Timber game as a counting problem ⋮ Ordinal Sums, Clockwise Hackenbush, and Domino Shave ⋮ The Polynomial Profile of Distance Games on Paths and Cycles ⋮ Enumeration by kernel positions for strongly Bernoulli type truncation games on words ⋮ Sterling Stirling play

Uses Software

• OEIS

Cites Work

• Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
• A degenerate Staudt-Clausen theorem
• Degenerate Bernoulli polynomials, generalized factorial sums, and their applications
• Explicit formulas for degenerate Bernoulli numbers
• Degenerate and \(n\)-adic versions of Kummer's congruences for values of Bernoulli polynomials
• A finite difference approach to degenerate Bernoulli and Stirling polynomials
• Duality between quasi-symmetric functions and the Solomon descent algebra
• The Cauchy numbers
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