Generating sets of certain finite subsemigroups of monotone partial bijections | Zendy

Leyla BUGAY | Zendy; Hayrullah Ayık | Zendy

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Generating sets of certain finite subsemigroups of monotone partial bijections

Author(s) -

Leyla BUGAY,

Hayrullah Ayık

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1710-86

Subject(s) - bijection, injection and surjection , mathematics , combinatorics , monotone polygon , order (exchange) , semigroup , identity (music) , bijection , discrete mathematics , geometry , physics , finance , acoustics , economics

Let In be the symmetric inverse semigroup, and let PODIn and POIn be its subsemigroups of monotone partial bijections and of isotone partial bijections on Xn = {1, . . . , n} under its natural order, respectively. In this paper we characterize the structure of (minimal) generating sets of the subsemigroups PODIn,r = {α ∈ PODIn : |im (α)| ≤ r} , POIn,r = {α ∈ POIn : |im (α)| ≤ r} , and En,r = {id A ∈ In : A ⊆ Xn and |A| ≤ r} where idA is the identity map on A ⊆ Xn for 0 ≤ r ≤ n− 1 .

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