A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider
the semigroup TF _ n TF n of all order-preserving transformations on an n-element zig-zag …

A fully invarient congruence relations on the free algebra on a given type induces a variety
of the given type. In contrast, a congruence relation of the free algebra provides algebra of …

For n∈ ℕ, let X n={a 1, a 2,…, an} be an n-element set and let F=(X n;< f) be a fence, also
called a zigzag poset. As usual, we denote by I n the symmetric inverse semigroup on X n …

GENERATING SETS OF SEMIGROUPS OF PARTIAL TRANSFORMATIONS PRESERVING
A ZIG-ZAG ORDER ON N Ilinka Dimitrova1, Jörg Koppitz2, Ladd Page 1 International …

Let Y be a fence of size m and r=⌊ m− 1/2⌊. The number b (m) of order-preserving
selfmappings of Y is equal to A rB rC rD r, where, if m is odd, A_r= 2 (r+ 1) ∑ s= 0^ r\left (4 …

Three results are obtained concerning the number of order preserving maps of an n-element
partially ordered set to itself. We show that any such ordered set has at least 2 2n/3 order …

The monoid of all partial injections on a finite set (the symmetric inverse semigroup) is of
particular interest because of the well-known Wagner-Preston Theorem. In this article, we …

Semigroups of order-preserving transformations have been extensively studied for finite
chains. We study the monoid OPN of all order-preserving partial transformations on the set N …

We study a submonoid of the well studied monoid\(POI_n\) of all order-preserving partial
injections on an n-element chain. The set\(IOF_n^{par}\) of all partial transformations …

A fence is a particular partial order on a (finite) set, close to the linear order. In this paper, we
calculate the rank of the semigroup FI _ n FI n of all order-preserving partial injections on an …