On relative ranks of finite transformation semigroups with restricted range

I. Dimitrova; J. Koppitz

doi:10.37863/umzh.v73i5.288

I. Dimitrova South-West University “Neofit Rilski”, Blagoevgrad, Bulgaria https://orcid.org/0000-0002-6078-5968
J. Koppitz Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Sofia, Bulgaria

DOI: https://doi.org/10.37863/umzh.v73i5.288

Ключові слова: transformation semigroups with restricted range, orderpreserving transformations, orientation-preserving transformations, relative rank, relative generating sets

Анотація

UDC 512.5

Про вiдноснi ранги напiвгруп фiнiтних перетворень з обмеженою областю значень

Визначено відносний ранг напівгрупи ${\scr T }(X, Y)$ усіх перетворень на скінченному ланцюгу $X$ з обмеженою областю значень $Y \subseteq X$ за модулем множини ${\scr OP }(X, Y )$ усіх перетворень у ${\scr T } (X, Y),$ що зберігають орієнтацію.
Крім того, встановлено відносний ранг напівгрупи ${\scr OP }(X, Y) $ за модулем множини ${\scr O}(X, Y)$ усіх перетворень в ${\scr OP }(X, Y),$ що зберігають порядок.
В обох випадках охарактеризовано відповідні мінімальні породжуючі множини.

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