    ## Generalized Derangements and Anagrams Without Fixed Letters. (arXiv:1810.07219v1 [math.CO])

In this paper we propose a combinatorial approach to generalized mathematical derangements and anagrams without fixed letters. In sections 1 and 2 we introduce the functions \$P\$ - the number of generalized derangements of a set, and \$P'\$ - the number of anagrams without fixed letters of a given word. The preliminary observations in these chapters provide the toolbox for developing two recursive algorithms in section 3 for computing \$P\$ and \$P'\$. The second algorithm leads to several different inequalities. They allow us to roughly estimate the values of \$P\$ and \$P'\$ and partially order them. The final section of this paper is dedicated to some number theoretical properties of \$P'.\$ The focus is on divisibility and the main technique is partitioning the anagrams into classes of equivalence in different ways. The article ends with a conjecture, which generalizes one of the theorems in the last chapter.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 In this paper we propose a combinatorial approach to generalized mathematical derangements and anagrams without fixed letters. In sections 1 and 2 we introduce the functions \$P\$ - the number of generalized derangements of a set, and \$P'\$ - the number of anagrams without fixed letters of a given word. The preliminary observations in these chapters provide the toolbox for developing two recursive algorithms in section 3 for computing \$P\$ and \$P'\$. The second algorithm leads to several different inequalities. They allow us to roughly estimate the values of \$P\$ and \$P'\$ and partially order them. The final section of this paper is dedicated to some number theoretical properties of \$P'.\$ The focus is on divisibility and the main technique is partitioning the anagrams into classes of equivalence in different ways. The article ends with a conjecture, which generalizes one of the theorems in the last chapter.
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