On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

We give a presentation for the monoid I O n of all order-preserving transformations of an n -chain whose ranges are intervals. We also consider the submonoid I O n - of I O n consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

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Veröffentlicht in:	Semigroup forum 2024-10, Vol.109 (2), p.336-346
1. Verfasser:	Fernandes, Vítor H.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Intervals Mathematics Mathematics and Statistics Monoids Research Article
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We give a presentation for the monoid I O n of all order-preserving transformations of an n -chain whose ranges are intervals. We also consider the submonoid I O n - of I O n consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.
ISSN:	0037-1912 1432-2137
DOI:	10.1007/s00233-024-10466-2