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Finite Symmetric Functions with Non-Trivial Arity Gap

Shtrakov, Slavcho, Koppitz, Jörg (2012)

Serdica Journal of Computing

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of...

Four-part semigroups - semigroups of Boolean operations

Prakit Jampachon, Yeni Susanti, Klaus Denecke (2012)

Discussiones Mathematicae - General Algebra and Applications

Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.

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