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 inGraphs and combinatorics Vol. 30; no. 1; pp. 159 - 170
Main Authors Eggleton, Roger B., Morayne, Michał
Format Journal Article
LanguageEnglish
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)
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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.
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-012-1261-0