Results 1 to 10 of about 132 (123)
Star factorizations and noncrossing partitions [PDF]
Discrete Mathematics, 2021 to appear in Discrete ...
Bridget Eileen Tenner
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Noncrossing partitions, toggles, and homomesy [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We introduce n(n − 1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions.
David Einstein +6 more
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On trees and noncrossing partitions
Discrete Applied Mathematics, 1998 Bijective proofs of some identities for partitions are given. In this paper a partition is a pair \({\mathbf P} =(P;\pi)\), with \(P\) a (finite) ground set together with a set-theoretical partition \[ \pi= \left\{P_1, \dots, P_k\left|\varnothing \neq P_i\subseteq P\text{ and }P = \bigcup^k_{i=1} P_i\right.\right\}.
Martin Klazar
exaly +3 more sources
On Noncrossing and Nonnesting Partitions of Type D [PDF]
Annals of Combinatorics, 2011 We present an explicit bijection between noncrossing and nonnesting partitions of Coxeter systems of type D which preserves openers, closers and transients.
Alessandro Conflitti, Ricardo Mamede
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Pairs of noncrossing free Dyck paths and noncrossing partitions
Discrete Mathematics, 2009 Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck
Richard P Stanley, William Y C Chen
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A group action on noncrossing partitions
Discrete Mathematics, 2013 Abstract Let NC n denote the set of noncrossing partitions of [ n ] = { 1 , 2 , … , n } . By defining a group action on the set NC n , we give a combinatorial interpretation of the expansion of the n -th Narayana polynomial on the basis { q k ( 1 + q ) n − 1 − 2 k
Hua Sun
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Bijections on two variations of noncrossing partitions [PDF]
Electronic Notes in Discrete Mathematics, 2009 We find bijections on 2-distant noncrossing partitions, 12312-avoiding partitions, 3-Motzkin paths, UH-free Schr{ö}der paths and Schr{ö}der paths without peaks at even height. We also give a direct bijection between 2-distant noncrossing partitions and 12312-avoiding partitions.
Jang Soo Kim
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Noncrossing Partitions of a Marked Surface
SIAM Journal on Discrete MathematicsWe define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces.
Nathan Reading
exaly +3 more sources
Tamari lattices and noncrossing partitions in type B
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Oriented Flip Graphs and Noncrossing Tree Partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Given a tree embedded in a disk, we define two lattices - the oriented flip graph of noncrossing arcs and the lattice of noncrossing tree partitions.
Alexander Garver, Thomas McConville
doaj +1 more source