恰好包含r对相交弧的对合线

IF 1 Q1 MATHEMATICS

Discrete Mathematics Letters Pub Date : 2022-06-04 DOI:10.47443/dml.2022.046

T. Mansour

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引用次数: 0

摘要

摘要研究了在n个字母上计数对合的生成函数Fr（x），该对合在它们的图形表示中恰好包含r对相交弧。更精确地说，给出了一种算法，用于计算任何给定r≥0的生成函数Fr（x）。为了导出给定r的结果，该算法对长度为2r+2且没有不动点的对合进行某些例行检查。该算法在Maple中实现，并给出了0≤r≤4的显式公式。

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Involutions containing exactly r pairs of intersecting arcs

Abstract The generating function Fr(x) that counts the involutions on n letters containing exactly r pairs of intersecting arcs in their graphical representation is studied. More precisely, an algorithm that computes the generating function Fr(x) for any given r ≥ 0 is presented. To derive the result for a given r, the algorithm performs certain routine checks on involutions of length 2r + 2 without fixed points. The algorithm is implemented in Maple and yields explicit formulas for 0 ≤ r ≤ 4.

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来源期刊

Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

12 weeks