Results 11 to 20 of about 1,690,008 (302)
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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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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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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Mathematics, 2023 In the paper, the authors briefly survey several generalizations of the Catalan numbers in combinatorial number theory, analytically generalize the Catalan numbers, establish an integral representation of the analytic generalization of the Catalan ...
Jian Cao +4 more
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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.
Bidkhori, Hoda, Sullivant, Seth
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A Note on q-analogue of Degenerate Catalan Numbers Associated with p-adic Integral on Zp
Symmetry, 2022 In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help of a fermionic p-adic q-integrals on Zp and establish some new connections with the degenerate Stirling numbers of the first and second kinds. Furthermore,
W. Khan
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Planar kinematics: cyclic fixed points, mirror superpotential, $k$-dimensional Catalan numbers, and root polytopes [PDF]
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, 2020 In this paper we prove that points in the space $X(k,n)$ of configurations of $n$ points in $\mathbb{CP}^{k-1}$ which are fixed under a certain cyclic action are the solutions to the generalized scattering equations on planar kinematics (PK).
F. Cachazo, Nick Early
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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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The Complexity of Trees, Universal Grammar and Economy Conditions
Biolinguistics, 2022 In this squib, I argue that the child faces a severe computational complexity problem in parsing even the simplest of trees: the number of possible trees consistent with UG grows exponentially as a function of the number of lexical items.
Chris Collins
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