scholarly journals Chain enumeration of k-divisible noncrossing partitions of classical types

2011 ◽  
Vol 118 (3) ◽  
pp. 879-898 ◽  
Author(s):  
Jang Soo Kim
Keyword(s):  
Noncrossing Partitions

scholarly journals Combinatorics of Exceptional Sequences in Type A

10.37236/6251 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Alexander Garver ◽  
Kiyoshi Igusa ◽  
Jacob P. Matherne ◽  
Jonah Ostroff
Keyword(s):  
Dynkin Diagram ◽  
Type A ◽  
Linear Extensions ◽  
Quiver Representations ◽  
Noncrossing Partitions ◽  
Underlying Graph ◽  
Exceptional Sequences

Exceptional sequences are certain sequences of quiver representations.  We introduce a class of objects called strand diagrams and use these to classify exceptional sequences of representations of a quiver whose underlying graph is a type $\mathbb{A}_n$ Dynkin diagram. We also use variations of these objects to classify $c$-matrices of such quivers, to interpret exceptional sequences as linear extensions of explicitly constructed posets, and to give a simple bijection between exceptional sequences and certain saturated chains in the lattice of noncrossing partitions. 

scholarly journals Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions

10.37236/232 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
D. Armstrong ◽  
C. Krattenthaler
Keyword(s):  
Euler Characteristic ◽  
Order Complex ◽  
Reflection Groups ◽  
Noncrossing Partitions ◽  
Minimal Elements ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Phd Thesis

The purpose of this paper is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted. As we show, the result on the Euler characteristic extends to generalized noncrossing partitions associated to well-generated complex reflection groups.

scholarly journals Pairs of noncrossing free Dyck paths and noncrossing partitions

2009 ◽  
Vol 309 (9) ◽  
pp. 2834-2838 ◽  
Author(s):  
William Y.C. Chen ◽  
Sabrina X.M. Pang ◽  
Ellen X.Y. Qu ◽  
Richard P. Stanley
Keyword(s):  
Noncrossing Partitions ◽  
Dyck Paths

scholarly journals From m-clusters to m-noncrossing partitions via exceptional sequences

2011 ◽  
Vol 271 (3-4) ◽  
pp. 1117-1139 ◽  
Author(s):  
Aslak Bakke Buan ◽  
Idun Reiten ◽  
Hugh Thomas
Keyword(s):  
Noncrossing Partitions ◽  
Exceptional Sequences

scholarly journals Noncrossing partitions for periodic braids

2017 ◽  
Vol 151 ◽  
pp. 36-50
Author(s):  
Eon-Kyung Lee ◽  
Sang-Jin Lee
Keyword(s):  
Noncrossing Partitions

scholarly journals A simple and direct derivation for the number of noncrossing partitions

1998 ◽  
Vol 126 (6) ◽  
pp. 1579-1581 ◽  
Author(s):  
S. C. Liaw ◽  
H. G. Yeh ◽  
F. K. Hwang ◽  
G. J. Chang
Keyword(s):  
Noncrossing Partitions ◽  
Direct Derivation

scholarly journals Enumeration of (k,2)-noncrossing partitions

2008 ◽  
Vol 308 (20) ◽  
pp. 4570-4577 ◽  
Author(s):  
Toufik Mansour ◽  
Simone Severini
Keyword(s):  
Noncrossing Partitions

scholarly journals Minimal factorizations of a cycle: a multivariate generating function

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Philippe Biane ◽  
Matthieu Josuat-Vergès
Keyword(s):  
Symmetric Group ◽  
Generating Function ◽  
Simple Formula ◽  
Hook Length ◽  
Noncrossing Partitions ◽  
Long Cycle ◽  
Number Of Factors ◽  
Multivariate Generalization ◽  
International Audience

International audience It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of k cycles of given lengths has a very simple formula: it is nk−1 where n is the rank of the underlying symmetric group and k is the number of factors. In particular, this is nn−2 for transposition factorizations. The goal of this work is to prove a multivariate generalization of this result. As a byproduct, we get a multivariate analog of Postnikov's hook length formula for trees, and a refined enumeration of final chains of noncrossing partitions.

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