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Combinatorics, probability & computing, ISSN 0963-5483, 07/2017, Volume 26, Issue 4, pp. 560 - 592
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights... 
Paper | MATHEMATICS | SCALING LIMITS | ORDERED TREES | STATISTICS | BIPARTITE PLANAR MAPS | FREE CONVOLUTION | TRIANGULATIONS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | GALTON-WATSON TREES | NONCROSSING PARTITIONS | BRIDGE | Partitions | Probability theory | Trees (mathematics) | Probability | Mathematics
Journal Article
The Electronic journal of combinatorics, ISSN 1077-8926, 2016, Volume 23, Issue 3
We introduce $n(n-1)/2$ natural involutions ("toggles") on the set $S$ of noncrossing partitions $\pi$ of size $n... 
Homomesy | Coxeter element | Involution | Noncrossing partition | Toggle group | MATHEMATICS | MATHEMATICS, APPLIED | noncrossing partition | homomesy | involution | toggle group
Journal Article
Journal of Combinatorial Theory. Series A, ISSN 0097-3165, 10/2017, Volume 151, pp. 36 - 50
... in the dual Garside structure by studying the combinatorics of noncrossing partitions arising from periodic braids... 
Dual Garside structure | Periodic braid | Noncrossing partition | Conjugacy problem | Braid group | MATHEMATICS | GARSIDE GROUPS | CONJUGACY | Mathematics - Geometric Topology
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 09/2013, Volume 20, Issue 3
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).... 
Catalan number | Noncrossing partition | Associahedron | Lattice path | MATHEMATICS, APPLIED | noncrossing partition | NUMBERS | IDEALS | MATHEMATICS | NON-CROSSING PARTITIONS | CLUSTER COMPLEXES | DIAGONAL INVARIANTS | lattice path | BOREL SUBALGEBRA | associahedron | QUOTIENT RING
Journal Article
ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 02/2018, Volume 25, Issue 1
For any finite Coxeter group W of rank n we show that the order complex of the lattice of non-crossing partitions NC(W... 
MATHEMATICS | generalized non-crossing partitions | MATHEMATICS, APPLIED | PARTIAL ORDER | buildings | Hurwitz graph | supersolvability | NONCROSSING PARTITIONS
Journal Article
Compositio mathematica, ISSN 0010-437X, 11/2009, Volume 145, Issue 6, pp. 1533 - 1562
We situate the noncrossing partitions associated with a finite Coxeter group within the context of the representation theory of quivers... 
reflections groups | noncrossing partitions | cluster category | quiver representations | torsion class | Dynkin quivers | Cambrian lattice | wide subcategories | semistable subcategories | SORTABLE ELEMENTS | TRIANGULATED CATEGORIES | MATHEMATICS | CLUSTERS | Theorems | Finite element analysis
Journal Article
by Sun, H
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 04/2020, Volume 101, Issue 2, pp. 186 - 200
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 05/2016, Volume 25, Issue 6, p. 1650035
We introduce a new basis of the Temperley–Lieb algebra. It is defined using a bijection between noncrossing partitions and fully commutative elements together... 
Temperley-Lieb algebra, noncrossing partitions, fully commutative elements, Artin braid group, dual braid monoid | ARTIN GROUPS | MATHEMATICS | ORDER | noncrossing partitions | Artin braid group | dual braid monoid | BRAID-GROUPS | Temperley-Lieb algebra | HECKE | fully commutative elements | COXETER GROUPS | Algebra
Journal Article
ANNALES DE L INSTITUT FOURIER, ISSN 0373-0956, 2019, Volume 69, Issue 5, pp. 2241 - 2289
.... In particular, we study the restriction of these orders to noncrossing partitions and show that the intervals for these orders can be enumerated in terms of the cluster complex... 
MATHEMATICS | Noncrossing partitions | cluster complex | SORTABLE ELEMENTS | Finite Coxeter groups | Bruhat order
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 02/2018, Volume 154, pp. 464 - 506
Our basic objects are partitions of finite sets of points into disjoint subsets. We investigate sets of partitions which are closed under taking tensor products, composition and involution, and which contain certain base partitions... 
Noncrossing partitions | Banica–Speicher quantum groups | Tensor category | Category of partitions | Easy quantum groups | MATHEMATICS | QUANTUM GROUPS | Banica-Speicher quantum groups | Combinatorics | Mathematics
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2013, Volume 365, Issue 8, pp. 4121 - 4151
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 20, pp. 4570 - 4577
A set partition is said to be ( k , d ) -noncrossing if it avoids the pattern 12 ⋯ k 12 ⋯ d... 
Partitions | Forbidden subsequences | Kernel method | partitions | MATHEMATICS | kernel method | TREES | forbidden subsequences | NONCROSSING PARTITIONS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 06/2012, Volume 312, Issue 11, pp. 1918 - 1922
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2017, Volume 45, Issue 1, pp. 81 - 127
We introduce and study a new action of the symmetric group $${\mathfrak {S}}_n$$ S n on the vector space spanned by noncrossing partitions of $$\{1, 2,\ldots , n\}$$ { 1 , 2 , … , n... 
Cyclic sieving | Noncrossing partition | Convex and Discrete Geometry | Symmetric group | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Skein relation | Combinatorics | Computer Science, general | Promotion | Rotation | MATHEMATICS | NUMBERS | INCREASING TABLEAUX
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 08/2017, Volume 27, Issue 5, pp. 455 - 475
In this paper, we present Gray codes for the sets of noncrossing partitions associated with the classical Weyl groups, and for the set of nonnesting partitions of type B... 
MATHEMATICS | Gray code | noncrossing partition | NON-CROSSING PARTITIONS | nonnesting partition | Hamilton cycle | Weyl groups
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 3/2012, Volume 35, Issue 2, pp. 313 - 343
... ≤0-configurations, studied by Buan, Reiten and Thomas, and noncrossing partitions of the Coxeter group associated to Q which are not contained in any proper standard parabolic subgroup... 
Mutations | Noncrossing partitions | Mathematics | Perpendicular categories | Derived category | Exceptional sequences | Hom-configurations | Reflection functors | Convex and Discrete Geometry | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Cluster combinatorics | Computer Science, general | Combinatorics | Quiver representations | MATHEMATICS | QUIVERS | Algebra
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 2019, Volume 23, Issue 3, pp. 483 - 492
We compute the representation theory of two families of noncrossing partition quantum groups connected to amalgamated free products and free wreath products... 
Compact quantum groups | Noncrossing partitions | Representation theory | MATHEMATICS | FREE WREATH PRODUCT
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2011, Volume 25, Issue 1, pp. 447 - 461
Let p be a set partition of [n] - {1, 2,..., n}. The standard representation of pi is the graph on the vertex set [n... 
Crossings and nestings | Noncrossing partitions | Catalan numbers | Set partitions | crossings and nestings | MATHEMATICS, APPLIED | noncrossing partitions | NESTINGS | set partitions | CROSSINGS | MATCHINGS | Studies | Graph representations | Mathematical analysis | Applied mathematics
Journal Article
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