Results 11 to 20 of about 132 (123)
Enumeration of bilaterally symmetric 3-noncrossing partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Schützenberger's theorem for the ordinary RSK correspondence naturally extends to Chen et. al's correspondence for matchings and partitions. Thus the counting of bilaterally symmetric $k$-noncrossing partitions naturally arises as an analogue for ...
Guoce Xin, Terence Y. J. Zhang
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$k$-distant crossings and nestings of matchings and partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We define and consider $k$-distant crossings and nestings for matchings and set partitions, which are a variation of crossings and nestings in which the distance between vertices is important. By modifying an involution of Kasraoui and Zeng (Electronic J.
Dan Drake, Jang Soo Kim
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A bijection between noncrossing and nonnesting partitions of types A and B [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{ n+1} \binom{2n}{n}$ when $\Psi =A_{n-1}$, and the binomial coefficient $\binom{2n}{n}$ when $\Psi =B_n$, and these numbers coincide with the correspondent ...
Ricardo Mamede
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$m$-noncrossing partitions and $m$-clusters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $W$ be a finite crystallographic reflection group, with root system $\Phi$. Associated to $W$ there is a positive integer, the generalized Catalan number, which counts the clusters in the associated cluster algebra, the noncrossing partitions for $W$,
Aslak Bakke Buan +2 more
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Discrete Mathematics & Theoretical Computer Science, 2020 The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter system are noncross- ing partitions, sortable elements, and cluster complexes. The first and the third of these have known Fuss–Catalan generalizations.
Christian Stump +2 more
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Bijections between noncrossing and nonnesting partitions for classical reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in
Alex Fink, Benjamin Iriarte Giraldo
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EL-Shellability of Generalized Noncrossing Partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In this article we prove that the poset of m-divisible noncrossing partitions is EL-shellable for every well-generated complex reflection group. This was an open problem for type G(d,d,n) and for the exceptional types, for which a proof is given case-by ...
Henri Mühle
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Rational Associahedra and Noncrossing Partitions [PDF]
The Electronic Journal of Combinatorics, 2013 Each positive rational number $x>0$ can be written uniquely as $x=a/(b-a)$ for coprime positive integers $0<a<b$. We will identify $x$ with the pair $(a,b)$. In this paper we define for each positive rational $x>0$ a simplicial complex $\mathsf{Ass}(x)=\mathsf{Ass}(a,b)$ called the rational associahedron. It is a pure simplicial complex of
Drew Armstrong +2 more
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A combinatorial model for exceptional sequences in type A [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya’s work) to classify exceptional sequences of representations of $Q$, the linearly
Alexander Garver, Jacob P. Matherne
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Tamari Lattices for Parabolic Quotients of the Symmetric Group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We present a generalization of the Tamari lattice to parabolic quotients of the symmetric group. More precisely, we generalize the notions of 231-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients, and
Henri Mühle, Nathan Williams
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