Results 1 to 10 of about 1,906 (92)

On the $H$-triangle of generalised nonnesting partitions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2014
With a crystallographic root system $\Phi$ , there are associated two Catalan objects, the set of nonnesting partitions $NN(\Phi)$, and the cluster complex $\Delta (\Phi)$. These possess a number of enumerative coincidences, many of which are captured in
Marko Thiel
doaj   +1 more source

$m$-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, Idun Reiten, Hugh Thomas   +2 more
doaj   +1 more source

Rational Catalan Combinatorics: The Associahedron [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
Each positive rational number $x>0$ can be written $\textbf{uniquely}$ as $x=a/(b-a)$ for coprime positive integers ...
Drew Armstrong, Brendon Rhoades, Nathan Williams   +2 more
doaj   +1 more source

Submaximal factorizations of a Coxeter element in complex reflection groups [PDF]

Discrete Mathematics & Theoretical Computer Science, 2011
When $W$ is a finite reflection group, the noncrossing partition lattice $NC(W)$ of type $W$ is a very rich combinatorial object, extending the notion of noncrossing partitions of an $n$-gon.
Vivien Ripoll
doaj   +1 more source

The $m$-Cover Posets and the Strip-Decomposition of $m$-Dyck Paths [PDF]

Discrete Mathematics & Theoretical Computer Science, 2014
In the first part of this article we present a realization of the $m$-Tamari lattice $\mathcal{T}_n^{(m)}$ in terms of $m$-tuples of Dyck paths of height $n$, equipped with componentwise rotation order. For that, we define the $m$-cover poset $\mathcal{P}
Myrto Kallipoliti, Henri Mühle
doaj   +1 more source

The dual of number sequences, Riordan polynomials, and Sheffer polynomials

Special Matrices, 2021
In this paper we introduce different families of numerical and polynomial sequences by using Riordan pseudo involutions and Sheffer polynomial sequences.
He Tian-Xiao, Ramírez José L.
doaj   +1 more source

From m-clusters to m-noncrossing partitions via exceptional sequences [PDF]

, 2011
Let W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number of noncrossing partitions for W.
Buan, Aslak Bakke, Reiten, Idun, Thomas, Hugh   +2 more
core   +3 more sources

A Unified Generalization of the Catalan, Fuss, and Fuss–Catalan Numbers

Mathematical and Computational Applications, 2019
In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss−Catalan numbers, and the Catalan−Qi function, and discover some properties of the unified generalization, including a product ...
Feng Qi, Xiao-Ting Shi, Pietro Cerone
doaj   +1 more source

Some Properties of the Fuss–Catalan Numbers

Mathematics, 2018
In the paper, the authors express the Fuss⁻Catalan numbers as several forms in terms of the Catalan⁻Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the ...
Feng Qi, Pietro Cerone
doaj   +1 more source

On a new congruence in the Catalan triangle [PDF]

Notes on Number Theory and Discrete Mathematics
For 0≤k≤n, the number C(n,k) represents the number of all lattice paths in the plane from the point (0,0) to the point (n,k), using steps (1,0) and (0,1), that never rise above the main diagonal y = x.
Jovan Mikić
doaj   +1 more source