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Semigroup Forum

, Volume 53, Issue 1, pp 351–368 | Cite as

Catalan monoids, monoids of local endomorphisms, and their presentations

  • Andrew Solomon
Research Article

Abstract

The Catalan monoid and partial Catalan monoid of a directed graph are introduced. Also introduced is the notion of a local endomorphism of a tree, and it is shown that the Catalan (resp. partial Catalan) monoid of a tree is simply its monoid of extensive local endomorphisms (resp. partial endomorphisms) of finite shift. The main results of this paper are presentations for the Catalan and partial Catalan monoids of a tree. Our presentation for the Catalan monoid of a tree is used to give an alternative proof for a result of Higgins. We also identify results of Aîzenštat and Popova which give presentations for the Catalan monoid and partial Catalan monoid of a finite symmetric chain.

Keywords

Inductive Hypothesis Directed Graph Elementary Transition Simple Root Finite Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • Andrew Solomon
    • 1
  1. 1.School of Mathematics and StatisticsF07, The University of SydneyAustralia

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