Catalan Monoids, Monoids of Local Endomorphisms, and Their Presentations
نویسنده
چکیده
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 nite shift. The main results of this paper are presentations for the Cata-lan 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 A zen stat and Popova which give presentations for the Catalan monoid and partial Catalan monoid of a nite symmetric chain.
منابع مشابه
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