Combinatorial Results for Certain Semigroups of Order-Decreasing Partial Isometries of a Finite Chain

Al-Kharousi, F.; Kehinde, R.; Umar, Abdullahi

doi:10.18642/jantaa_7100121902

Cited by 7 publications

(11 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is well known that I n is an inverse semigroup and every finite inverse semigroup S is embeddable in I n , the analog of Cayley's theorem for finite groups. Hence, as emphasized in [1], the importance of I n to inverse semigroup theory is similar to that of the symmetric group S n to group theory. Moreover, Gomes and Howie remarked in [11] that very little has been written on the symmetric inverse semigroups.…”

Section: Introductionmentioning

confidence: 91%

Relative ranks of some partial transformation semigroups

Yiğit¹,

Ayık²,

Ayık³

2019

Turk J Math

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 91%

Relative ranks of some partial transformation semigroups

Yiğit¹,

Ayık²,

Ayık³

2019

Turk J Math

View full text Add to dashboard Cite

“…. , n} was initiated by Al-Kharousi et al [3,4]. The first of these two papers is dedicated to investigating some combinatorial properties of the monoid DP n and of its submonoid ODP n of all order-preserving (considering the usual order of N) partial isometries, in particular, their cardinalities.…”

Section: Introductionmentioning

confidence: 99%

On the monoid of partial isometries of a cycle graph

Fernandes¹,

Paulista²

2022

Preprint

View full text Add to dashboard Cite

In this paper we consider the monoid DPC n of all partial isometries of a n-cycle graph C n . We show that DPC n is the submonoid of the monoid PORI n of all oriented partial permutations on a n-chain whose elements are precisely all restrictions of the dihedral group of order 2n. For this purpose, a useful characterization of an oriented transformation is established first. Our main aims are to determine the rank and to exhibit a presentation of DPC n . We also describe Green's relations of DPC n and calculate its cardinal. 2020 Mathematics subject classification: 20M20,

show abstract

“…Hence, the importance of I n in inverse semigroup theory is similar to the importance of S n in group theory. Although the semigroup I n has been extensively studied (see, for example, [1,5,10,14]), there are still many interesting problems concerning I n to be investigated.…”

Section: Introductionmentioning

confidence: 99%

Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups

Bugay¹

2021

Turk J Math

View full text Add to dashboard Cite

Let In and Sn be the symmetric inverse semigroup and the symmetric group on a finite chain Xn = {1,. .. , n} , respectively. Also let In,r = {α ∈ In : |im(α)| ≤ r} for 1 ≤ r ≤ n − 1. For any α ∈ In , if α = α 2 = α 4 then α is called a quasi-idempotent. In this paper, we show that the quasi-idempotent rank of In,r (both as a semigroup and as an inverse semigroup) is n 2 if r = 2 , and n r + 1 if r ≥ 3. The quasi-idempotent rank of In,1 is n (as a semigroup) and n − 1 (as an inverse semigroup).

show abstract

Combinatorial Results for Certain Semigroups of Order-Decreasing Partial Isometries of a Finite Chain

Abstract: (left) waist, right (left) shoulder and fix of a transformation, idempotents and nilpotents.

Cited by 7 publications

References 14 publications

Relative ranks of some partial transformation semigroups

Relative ranks of some partial transformation semigroups

On the monoid of partial isometries of a cycle graph

Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups

Contact Info

Product

Resources

About