Combinatorial results of collapse for order-preserving and order-decreasing transformations

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dc.contributor.authorKorkmaz, Emrah
dc.contributor.departmentOthertr_TR
dc.contributor.facultyOthertr_TR
dc.date.accessioned2022-12-28T13:00:58Z
dc.date.available2022-12-28T13:00:58Z
dc.date.issued2022
dc.description.abstractThe full transformation semigroup Tn is defined to consist of all functions from Xn={1,…,n} to itself, under the operation of composition. In \cite{JMH1}, for any α in Tn, Howie defined and denoted collapse by c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}. Let On be the semigroup of all order-preserving transformations and Cn be the semigroup of all order-preserving and decreasing transformations on Xn under its natural order, respectively. Let E(On) be the set of all idempotent elements of On, E(Cn) and N(Cn) be the sets of all idempotent and nilpotent elements of Cn, respectively. Let U be one of {Cn,N(Cn),E(Cn),On,E(On)}. For α∈U, we consider the set \imc(α)={t∈\im(α):|tα−1|≥2}. For positive integers 2≤k≤r≤n, we define U(k)={α∈U:t∈\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):∣∣⋃t∈\imc(α)tα−1|=r}. The main objective of this paper is to determine |U(k,r)|, and so |U(k)| for some values r and k.tr_TR
dc.description.indexTrdizintr_TR
dc.identifier.endpage777tr_TR
dc.identifier.issn/e-issn1303-5991
dc.identifier.issue3tr_TR
dc.identifier.startpage769tr_TR
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.1019458tr_TR
dc.identifier.urihttp://hdl.handle.net/20.500.12575/86562
dc.identifier.volume71tr_TR
dc.language.isoentr_TR
dc.publisherAnkara Üniversitesitr_TR
dc.relation.isversionof10.31801/cfsuasmas.1019458tr_TR
dc.relation.journalCommunications, Series A1:Mathematics and Statisticstr_TR
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıtr_TR
dc.subjectOrder-preserving/decreasing transformation, collapse, nilpotent, idempotenttr_TR
dc.titleCombinatorial results of collapse for order-preserving and order-decreasing transformationstr_TR
dc.typeArticletr_TR

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