The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence

Fernandes, Vítor H.; Koppitz, Jörg; Musunthia, Tiwadee

doi:10.1007/s40840-017-0598-1

Cited by 23 publications

(16 citation statements)

References 15 publications

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“…The survey [10] presents these results and similar ones for other classes of transformation monoids, in particular, for monoids of order-preserving transformations and for some of their extensions. More recently, for instance, the papers [1,2,5,[11][12][13][14][15]23,33,34] are dedicated to the computation of the ranks of certain (classes of transformation) semigroups or monoids. Now, let G = (V , E) be a simple graph (i.e.…”

Section: Introductionmentioning

confidence: 99%

Partial automorphisms and injective partial endomorphisms of a finite undirected path

et al. 2021

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In this paper, we study partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of the monoids IEnd(P n ) and PAut(P n ) of all injective partial endomorphisms and of all partial automorphisms of the undirected path P n with n vertices. We also describe Green's relations of PAut(P n ) and IEnd(P n ) and calculate their cardinals. Keywords Injective partial endomorphismsThis work is funded by national funds through the FCT -Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications).

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Section: Introductionmentioning

confidence: 99%

Partial automorphisms and injective partial endomorphisms of a finite undirected path

et al. 2021

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“…For example, the rank of the extensively studied monoid of all order-preserving transformations of a n-chain is n. This result was proved by Gomes and Howie [12] in 1992. More recently, for instance, the papers [1,8,9,10,11,26] are dedicated to the computation of the ranks of certain classes of transformation semigroups or monoids.…”

Section: Introductionmentioning

confidence: 99%

On the Rank of Monoids of Endomorphisms of a Finite Directed Path

Fernandes¹,

Paulista²

2021

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In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid wEnd P n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid O n of all order-preserving transformations of a n-chain. Also, we describe the regular elements of wEnd P n and calculate its size and number of idempotents.

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“…On the other hand, an exact formula for the number of endomorphisms on (n, ) for even as well as odd n was given in [13]. Recently, in [8], the authors determine the rank of T F n . Recall that the rank of a semigroup S, denoted by rankS, is the minimal size of a generating set of S, rankS := min{|A| : A ⊆ S, A generates S}.…”

Section: Introductionmentioning

confidence: 99%