A Note on Counting Homomorphisms of Paths

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...

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Bibliographic Details
Published in:	Graphs and combinatorics Vol. 30; no. 1; pp. 159 - 170
Main Authors:	Eggleton, Roger B., Morayne, Michał
Format:	Journal Article
Language:	English
Published:	Tokyo Springer Japan 2014 Springer Nature B.V
Subjects:	Combinatorial analysis Combinatorics Counting Engineering Design Exact solutions Graphs Homomorphisms Mathematical analysis Mathematics Mathematics and Statistics Original Paper Path Generating function Endomorphism Catalan number 60G50 (secondary) Homomorphism 05A15 (primary)
Online Access:	Get full text
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Summary:	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.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	0911-0119 1435-5914
DOI:	10.1007/s00373-012-1261-0