Enumeration by kernel positions for strongly Bernoulli type truncation games on words

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Hetyei, Gabor

关键词: Bernoulli polynomials;    Progressively finite games;    Kernel position;    Enumerative combinatorics;    Generating functions;   

DOI  :  10.1016/j.jcta.2010.01.003

来源: Elsevier

【 摘 要 】

We find the winning strategy for a class of truncation games played on words. As a consequence of the present author's recent results on some of these games we obtain new formulas for Bernoulli numbers and polynomials of the second kind and a new combinatorial model for the number of connected permutations of given rank. For connected permutations, the decomposition used to find the winning strategy is shown to be bijectively equivalent to King's decomposition, used to recursively generate a transposition Gray code of the connected permutations. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free