Abstract
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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The on-line encyclopedia of integer sequences. The OEIS Foundation. http://oeis.org/
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Eggleton, R.B., Morayne, M. A Note on Counting Homomorphisms of Paths. Graphs and Combinatorics 30, 159–170 (2014). https://doi.org/10.1007/s00373-012-1261-0
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DOI: https://doi.org/10.1007/s00373-012-1261-0