Главными инструментами математической кибернетики являются дискретная
математика и алгебра. Основные понятия и свойства математических структур этих …

A fence is an ordered set that the order forms a path with alternating orientation. Let F=(F;
${\leq} $) be a fence and let OT (F) be the semigroup of all order-preserving self-mappings of …

Abstract In [25], a discrete homotopy theory for reflexive digraphs was developed. In the
present paper, we prove that if a finite, connected reflexive digraph X has non-trivial …

Corresponding to each ordered set there is a variety, determined up to equivalence,
generated by an algebra whose term operations are all the monotone operations on the …

E. Corominas introduced recently this notion for posets: P is projective if every map f from P
2 to P which is order preserving and idempotent (ie f (x, x)= x for all x ε P) is a projection. We …

It is well known that the transformation semigroup on a nonempty set $ X $, which is denoted
by $ T (X) $, is regular, but its subsemigroups do not need to be. Consider a finite ordered …

It is well known that the semigroup T (X) of all transformations on a set X is regular, but its
subsemigroups do not need to be. Consider an ordered set (X; ≤)(X;≤) whose order forms …

We define nonextendible colored posets and zigzags of a poset. These notions are related
to the earlier notions of gaps, holes, obstructions and zigzags considered by Duffus …

We prove that if a finite connected poset admits an order-preserving Taylor operation, then
all of its homotopy groups are trivial. We use this to give new characterisations of locally …

A finite, nontrivial algebra is order-primal if its term functions are precisely the monotone
functions for some order on the underlying set. We show that the prevariety generated by an …