LAUSR

Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy

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0 Published in 2021 at "Letters in Mathematical Physics"

DOI: 10.1007/s11005-021-01391-4

Abstract: We consider the Dubrovin–Frobenius manifold of rank 2 whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces,… read more here.

Keywords: extended nonlinear; dinger hierarchy; nonlinear schr; catalan numbers ... See more keywords

ON THE DIVISIBILITY OF SUMS OF q-SUPER CATALAN NUMBERS

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1 Published in 2023 at "Bulletin of the Australian Mathematical Society"

DOI: 10.1017/s0004972723000400

Abstract: The integrality of the numbers $A_{n,m}={(2n)!(2m)!}/{n!m!(n+m)!}$ was observed by Catalan as early as 1874 and Gessel named $A_{n,m}$ the super Catalan numbers. The positivity of the q-super Catalan numbers (q-analogue of the super Catalan numbers)… read more here.

Keywords: sums super; divisibility sums; catalan numbers; super catalan ... See more keywords

Volterra Chain and Catalan Numbers

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1 Published in 2018 at "JETP Letters"

DOI: 10.1134/s0021364018240013

Abstract: We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in… read more here.

Keywords: catalan numbers; volterra chain; chain catalan;

Binomial sums involving Catalan numbers

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1 Published in 2021 at "Rocky Mountain Journal of Mathematics"

DOI: 10.1216/rmj.2021.51.1221

Abstract: Recently, various interesting binomial sums involving Catalan numbers have been derived and computed. Inspired from them, several binomial sums involving Catalan numbers are evaluated in closed forms using a hypergeometric series approach. read more here.

Keywords: binomial sums; catalan numbers; involving catalan; sums involving ... See more keywords

A Note on the Sequence Related to Catalan Numbers

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1 Published in 2019 at "Symmetry"

DOI: 10.3390/sym11030371

Abstract: The main purpose of this paper is to find explicit expressions for two sequences and to solve two related conjectures arising from the recent study of sums of finite products of Catalan numbers by Zhang… read more here.

Keywords: related catalan; catalan numbers; note sequence; sequence related ... See more keywords