For any integer n ≥ 2, let R0(n + 1) be the class of 0-semihypergroups H of size n + 1 such that {y} ⊆ xy ⊆ {0, y} for all x, y ∈ H - {0}, all subsemihypergroups K ⊆ H are 0-simple and, when |K| ≥ 3, the fundamental relation βK is not transitive. We determine a transversal of isomorphism classes of semihypergroups in R0(n + 1) and we prove that its cardinality is the (n + 1)-th term of sequence A000070 in [21], namely, ∑n k=0 p(k), where p(k) denotes the number of non-increasing partitions of integer k. © 2016 Old City Publishing, Inc.

A family of 0-simple semihypergroups related to sequence A000070

DE SALVO, Mario
Primo
;
LO FARO, Giovanni
Ultimo
2016-01-01

Abstract

For any integer n ≥ 2, let R0(n + 1) be the class of 0-semihypergroups H of size n + 1 such that {y} ⊆ xy ⊆ {0, y} for all x, y ∈ H - {0}, all subsemihypergroups K ⊆ H are 0-simple and, when |K| ≥ 3, the fundamental relation βK is not transitive. We determine a transversal of isomorphism classes of semihypergroups in R0(n + 1) and we prove that its cardinality is the (n + 1)-th term of sequence A000070 in [21], namely, ∑n k=0 p(k), where p(k) denotes the number of non-increasing partitions of integer k. © 2016 Old City Publishing, Inc.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3094001
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