A Note on Counting Homomorphisms of Paths

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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Veröffentlicht in:Graphs and combinatorics 2014, Vol.30 (1), p.159-170
Hauptverfasser: Eggleton, Roger B., Morayne, Michał
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Combinatorics
Counting
Engineering Design
Exact solutions
Graphs
Homomorphisms
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung: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.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-012-1261-0