Scholarlink

<p>We call a permutation to be of odd order if writing in cycle form consisting of only odd cycles, and call a permutation to be a Callan permutation if all its left-to-right minima appear at odd positions. This paper aims to provide five elementary proofs that Callan permutations and odd order permutations have the same cardinality: one by generating functions, two by recursions and another two by combinatorial bijections. The last bijection gives rise to a refinement of this equality.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Callan permutations and odd order permutations

  • 期刊论文

  • 发表日期：

    2025年10月30日

查看全文
  • Rosena R. X. Du,
  • Zhicong Lin,
  • David G. L. Wang,
  • Tongyuan Zhao

摘要

We call a permutation to be of odd order if writing in cycle form consisting of only odd cycles, and call a permutation to be a Callan permutation if all its left-to-right minima appear at odd positions. This paper aims to provide five elementary proofs that Callan permutations and odd order permutations have the same cardinality: one by generating functions, two by recursions and another two by combinatorial bijections. The last bijection gives rise to a refinement of this equality.