Involutions containing exactly r pairs of intersecting arcs

Toufik Mansour

doi:10.47443/dml.2022.046

Involutions containing exactly r pairs of intersecting arcs

Toufik Mansour

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

The generating function F_r(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 F_r(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.

Original language	American English
Pages (from-to)	64-67
Number of pages	4
Journal	Discrete Mathematics Letters
Volume	10
DOIs	https://doi.org/10.47443/dml.2022.046
State	Published - 2022

Keywords

arc-pattern 3412
involution

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.47443/dml.2022.046

Cite this

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title = "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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AB - 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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KW - involution

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U2 - 10.47443/dml.2022.046

DO - 10.47443/dml.2022.046

M3 - Article

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SP - 64

EP - 67

JO - Discrete Mathematics Letters

JF - Discrete Mathematics Letters

ER -

Involutions containing exactly r pairs of intersecting arcs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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