Combinatorial results for geometric structures in endomorphism semiring

Abstract

This paper is a continuation of [8]. Here we find some combinatorial results for strings and triangles.

Jordan derivations in finite endomorphism semirings

“…From [15] we know that any endomorphism α ∈ △ (n) {a, b, c} can be characterized by ordered triple (x, y, z), where α(a) = x, α(b) = y and α(c) = z and x, y, z ∈ {a, b, c} and this triple is called a type of α. This is denoted by α ∈ (x, y, z).…”

“…We remind that the type (a, b, c), that is the subsemiring of the right identities of △ (n) {a, b, c} is denoted by RI △ (n) {a, b, c} in [15].…”

“…The endomorphism semirings of a finite semilattice are well-established, see [13], [14] and [15]. Basic facts for semirings can be found in [4].…”