Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584738 | Journal of Algebra | 2014 | 23 Pages |
Abstract
Fully simple semihypergroups have been introduced in [9], motivated by the study of the transitivity of the fundamental relation β in semihypergroups. Here, we determine a transversal of isomorphism classes of fully simple semihypergroups with a right absorbing element. The structure of that transversal can be described by means of certain transitive, acyclic digraphs. Moreover, we prove that, if n is an integer ≥2, then the number of isomorphism classes of fully simple semihypergroups of size n+1n+1, with a right absorbing element, is the (n+1)(n+1)-th term of sequence A000712 in [20], namely, ∑k=0np(k)p(n−k), where p(k)p(k) denotes the number of nonincreasing partitions of integer k.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mario De Salvo, Dario Fasino, Domenico Freni, Giovanni Lo Faro,