A Note on Counting Homomorphisms of Paths |
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| Authors: | Roger B Eggleton Michał Morayne |
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| Institution: | 1. Department of Mathematics, Illinois State University, Normal, IL, 61790, USA
2. Institute of Mathematics and Computer Science, Wroc?aw University of Technology, Wybrze?e Wyspiańskiego 27, 50-370, Wroc?aw, Poland
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| 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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