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