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Abstract: In this paper we elaborate on the structure of the semigroup tree and theregularities on the number of descendants of each node observed earlier. Theseregularites admit two different types of behavior and in this work weinvestigate which of the two types takes place in particular for well-knownclasses of semigroups. Also we study the question of what kind of chains appearin the tree and characterize the properties like being infinite thereof. Weconclude with some thoughts that show how this study of the semigroup tree mayhelp in solving the conjecture of Fibonacci-like behavior of the number ofsemigroups with given genus.



Author: Maria Bras-Amoros, Stanislav Bulygin

Source: https://arxiv.org/



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