scholarly journals Integer Partitions and Binary Trees

2002 ◽  
Vol 28 (3-4) ◽  
pp. 592-601 ◽  
Author(s):  
Frank Schmidt

10.37236/9446 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Shane Chern

In this paper, we start by considering generating function identities for linked partition ideals in the setting of basic graph theory. Then our attention is turned to $q$-difference systems, which eventually lead to a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews--Gordon type generating function identities. These proofs also have an interesting connection with binary trees. Further, we give illustrations of constructing a linked partition ideal, or more loosely, a set of integer partitions whose generating function corresponds to a given set of special $q$-multi-summations.



Author(s):  
Ro-Yu WU ◽  
Jou-Ming CHANG ◽  
Sheng-Lung PENG ◽  
Chun-Liang LIU
Keyword(s):  




1980 ◽  
Vol 15 (6) ◽  
pp. 64-67 ◽  
Author(s):  
Abha Moitra


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Riccardo Conti ◽  
Davide Masoero

Abstract We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model.We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.



Author(s):  
Biagio Cosenza ◽  
Gennaro Cordasco ◽  
Rosario De Chiara ◽  
Ugo Erra ◽  
Vittorio Scarano
Keyword(s):  


2017 ◽  
Vol 695 ◽  
pp. 42-53
Author(s):  
Axel Bacher ◽  
Olivier Bodini ◽  
Alice Jacquot
Keyword(s):  


1993 ◽  
Vol 2 (2) ◽  
pp. 145-156 ◽  
Author(s):  
Philippe Flajolet ◽  
Zhicheng Gao ◽  
Andrew Odlyzko ◽  
Bruce Richmond

The number, , of rooted plane binary trees of height ≤ h with n internal nodes is shown to satisfyuniformly for δ−1(log n)−1/2 ≤ β ≤ δ(log n)1/2, where and δ is a positive constant. An asymptotic formula for is derived for h = cn, where 0 < c < 1. Bounds for are also derived for large and small heights. The methods apply to any simple family of trees, and the general asymptotic results are stated.



1984 ◽  
Vol 103 (2) ◽  
pp. 461-480 ◽  
Author(s):  
Boris Pittel


Sign in / Sign up

Export Citation Format

Share Document