A Note on Counting Homomorphisms of Paths

被引：1

作者：

Eggleton, Roger B. ^{[1
]}

Morayne, Michal ^{[2
]}

机构：

[1] Illinois State Univ, Dept Math, Normal, IL 61790 USA

[2] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

GRAPHS AND COMBINATORICS | 2014年 / 30卷 / 01期

关键词：

Path; Homomorphism; Generating function; Catalan number; Endomorphism; ALGORITHM; NUMBER;

D O I：

10.1007/s00373-012-1261-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain two identities and an explicit formula for the number of homomorphisms of a finite path into a finite path. For the number of endomorphisms of a finite path these give over-count and under-count identities yielding the closed-form formulae of Myers. We also derive finite Laurent series as generating functions which count homomorphisms of a finite path into any path, finite or infinite.

引用

页码：159 / 170

页数：12

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