منابع مشابه
Double Catalan Monoids
In this paper we define and study what we call the double Catalan monoid. This monoid is the image of a natural map from the 0-Hecke monoid to the monoid of binary relations. We show that the double Catalan monoid provides an algebraization of the (combinatorial) set of 4321-avoiding permutations and relate its combinatorics to various off-shoots of both the combinatorics of Catalan numbers and...
متن کاملCatalan Monoids, Monoids of Local Endomorphisms, and Their Presentations
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...
متن کاملIntonational encoding of double negation in Catalan
In this paper we shall explore the phenomenon of double negation (DN) in a negative concord language like Catalan from an inferential perspective. According to recent developments within the generative approach to the theory of sentential grammar, a proper account of this phenomenon requires an analysis of the lexical, syntactic, and semantic conditions involved. Yet this model only attempts to...
متن کاملGarside monoids vs divisibility monoids
Divisibility monoids (resp. Garside monoids) are a natural algebraic generalization of Mazurkiewicz trace monoids (resp. spherical Artin monoids), namely monoids in which the distributivity of the underlying lattices (resp. the existence of common multiples) is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be commutations (resp. be of Coxeter ty...
متن کاملCatalan structures and Catalan pairs
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced in [DFPR] with the aim of giving a common language to most of the structures counted by Catalan numbers. Here, we give a simple method to pass from the recursive definition of a generic Catalan structure to the recursive definitio...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2011
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-011-0336-y