关于每个循环赋权 $-1$ 的排列与 D-排列的连分数的一个注记
组合数学
2024-04-19 v2
摘要
我们证明了，当每个循环被赋予权重 时，枚举具有大量独立统计量的排列或 D-排列的常生成函数可以得到非常简单的连分数。证明基于一个简单的引理，该引理将循环数模 2 的同余类与不动点数、循环峰（或循环谷）数以及交叉数联系起来。
引用
@article{arxiv.2306.11500,
title = {A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle},
author = {Bishal Deb and Alan D. Sokal},
journal= {arXiv preprint arXiv:2306.11500},
year = {2024}
}
备注
LaTeX2e, 25 pages, includes 4 figures. Version 2 (34 pages, 6 figures) contains a slightly expanded introduction and a pair of running examples; to appear in the Electronic Journal of Combinatorics. arXiv admin note: text overlap with arXiv:2304.06545, arXiv:2212.07232, arXiv:2003.08192