منابع مشابه
Tamari lattices and noncrossing partitions in type B
The usual, or type An, Tamari lattice is a partial order on T A n , the triangulations of an (n+3)-gon. We define a partial order on T B n , the set of centrally symmetric triangulations of a (2n + 2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the An Tamari lattice, and therefore that it deserves to be considered the Bn Tamari lattice. We define a bij...
متن کاملTamari lattices and noncrossing partitions in type B and D
The usual, or type An, Tamari lattice is a partial order on T A n , the triangulations of an (n+3)-gon. We define a partial order on T B n , the set of centrally symmetric triangulations of a (2n + 2)-gon. We show that it is a lattice, and that it shares certain other nice properties of the An Tamari lattice, and therefore that it deserves to be considered the Bn Tamari lattice. We define a bij...
متن کاملGeometry of ν-Tamari lattices in types A and B
In this extended abstract, we exploit the combinatorics and geometry of triangulations of products of simplices to reinterpret and generalize a number of constructions in Catalan combinatorics. In our framework, the main role of “Catalan objects” is played by (I, J)-trees: bipartite trees associated to a pair (I, J) of finite index sets that stand in simple bijection with lattice paths weakly a...
متن کاملthe investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
A self-dual poset on objects counted by the Catalan numbers and a type-B analogue
We introduce two partially ordered sets, P n and P B n , of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of P n and P B n are subsets of the symmetric and the hyperoctahedral groups, consisting of permutations which avoid certain patterns. The order relation is given by (strict) containment of the descent sets. In each case, by means of an expl...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/j.dam.2003.11.001