Results 11 to 20 of about 112,655 (271)

The $(m, n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q, t$-symmetry [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area; skip; dinv) are given, we have an algorithm to construct the marked ...
Ryan Kaliszewski, Huilan Li
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Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function

Results in Nonlinear Analysis, 2021
In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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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, Idun Reiten, Hugh Thomas   +2 more
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Factors of alternating convolution of the Gessel numbers [PDF]

Notes on Number Theory and Discrete Mathematics
The Gessel number P(n,r) is the number of lattice paths in the plane with (1,0) and (0,1) steps from (0,0) to (n+r, n+r-1) that never touch any of the points from the set {(x,x)∈ℤ²:x≥r}. We show that there is a close relationship between Gessel numbers P(
Jovan Mikić
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Modular Catalan numbers

European Journal of Combinatorics, 2017
Minor ...
Nickolas Hein, Jia Huang
openaire   +3 more sources

Symmetry of Narayana Numbers and Rowvacuation of Root Posets

Forum of Mathematics, Sigma, 2021
For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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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
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Three Identities of the Catalan-Qi Numbers

Mathematics, 2016
In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.
Mansour Mahmoud, Feng Qi
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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
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New Expressions for Sums of Products of the Catalan Numbers

Axioms, 2021
In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan ...
Conghui Xie, Yuan He
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