Fully simple semihypergroups have been introduced in , 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 + 1, with a right absorbing element, is the (n + 1)-th term of sequence A000712 in , namely , ∑_(k=0)^n▒〖p(k)p(n-k), where p(k) denotes the number of nonincreasing partitions of integer k.
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