Results 21 to 30 of about 1,655,826 (313)
Knight's paths towards Catalan numbers [PDF]
Discrete Mathematics, 2022 We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the $x$-axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection ...
Jean-Luc Baril, J. L. Ramírez
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Bogoyavlensky Lattices and Generalized Catalan Numbers [PDF]
Russian journal of mathematical physics, 2022 We study the problem of the decay of initial data in the form of a unit step for the Bogoyavlensky lattices. In contrast to the Gurevich–Pitaevskii problem of the decay of initial discontinuity for the KdV equation, it turns out to be exactly solvable ...
V. E. Adler
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Refinements of the braid arrangement and two-parameter Fuss–Catalan numbers [PDF]
Journal of Algebraic Combinatorics, 2022 A hyperplane arrangement in $${\mathbb {R}}^n$$ R n is a finite collection of affine hyperplanes. Counting regions of hyperplane arrangements is an active research direction in enumerative combinatorics.
Priyavrat Deshpande +2 more
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Catalan numbers as discrepancies for a family of substitutions on infinite alphabets [PDF]
Indagationes mathematicae, 2022 In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets.
D. Frettlöh, A. Garber, Neil Mañibo
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Revisiting Catalan Numbers: An AB2 Polymerization Perspective [PDF]
, 2022 Number sequences, like Fibonacci, Fermat, Markov, Euler, Bernoulli, etc., have been popular in exemplifying a variety of scientific phenomena. Here, we explore the Catalan numbers in the context of ABm step polymerisation and develop a framework to ...
Ravi Anand, Singh +3 more
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Divisibility of generalized Catalan numbers [PDF]
Journal of Combinatorial Theory, Series A, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Konvalinka, Konvalinka, Matjaž
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Generalized Catalan Numbers from Hypergraphs [PDF]
Electronic Journal of Combinatorics, 2021 The Catalan numbers $C_{n} \in \{1,1,2,5,14,42,\dots \}$ form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting rooted plane ...
Paul E. Gunnells
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Positroid Catalan numbers [PDF]
Communications of the American Mathematical Society, 2021 Given a (bounded affine) permutation f f , we study the positroid Catalan number C f C_f defined to be the torus-equivariant Euler characteristic of the associated open positroid variety.
Pavel Galashin, T. Lam
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Eulerian-Catalan Numbers [PDF]
The Electronic Journal of Combinatorics, 2011 We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.
Hoda Bidkhori, Seth Sullivant
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Noncommutative Catalan Numbers [PDF]
Annals of Combinatorics, 2019 The goal of this paper is to introduce and study noncommutative Catalan numbers $C_n$ which belong to the free Laurent polynomial algebra in $n$ generators. Our noncommutative numbers admit interesting (commutative and noncommutative) specializations, one of them related to Garsia-Haiman $(q,t)$-versions, another -- to solving noncommutative quadratic ...
Berenstein, A., Retakh, V.
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