scholarly journals Integer Partitions and Binary Trees

2002 ◽  
Vol 28 (3-4) ◽  
pp. 592-601 ◽  
Author(s):  
Frank Schmidt
Keyword(s):  
Binary Trees ◽  
Integer Partitions

scholarly journals Linked Partition Ideals, Directed Graphs and $q$-Multi-Summations

10.37236/9446 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Shane Chern
Keyword(s):  
Graph Theory ◽  
Generating Function ◽  
Directed Graphs ◽  
Binary Trees ◽  
Computer Assisted ◽  
Integer Partitions ◽  
Factorization Problem ◽  
Difference Systems ◽  
Interesting Connection ◽  
Basic Graph

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.

Gray-Code Ranking and Unranking on Left-Weight Sequences of Binary Trees

2016 ◽  
Vol E99.A (6) ◽  
pp. 1067-1074 ◽  
Author(s):  
Ro-Yu WU ◽  
Jou-Ming CHANG ◽  
Sheng-Lung PENG ◽  
Chun-Liang LIU
Keyword(s):  
Gray Code ◽  
Binary Trees

scholarly journals On Conjectures Concerning the Smallest Part and Missing Parts of Integer Partitions

2021 ◽  
Author(s):  
Damanvir Singh Binner ◽  
Amarpreet Rattan
Keyword(s):  
Integer Partitions

A note on algebraic specification of binary trees

1980 ◽  
Vol 15 (6) ◽  
pp. 64-67 ◽  
Author(s):  
Abha Moitra
Keyword(s):  
Binary Trees ◽  
Algebraic Specification

scholarly journals Counting monster potentials

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Riccardo Conti ◽  
Davide Masoero
Keyword(s):  
Excited States ◽  
Ground State ◽  
Hermite Polynomials ◽  
Large Momentum ◽  
Integer Partitions ◽  
Complex Equilibria ◽  
State Potential

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.

Load Balancing in Mesh-like Computations using Prediction Binary Trees

2008 ◽  
Author(s):  
Biagio Cosenza ◽  
Gennaro Cordasco ◽  
Rosario De Chiara ◽  
Ugo Erra ◽  
Vittorio Scarano
Keyword(s):  
Load Balancing ◽  
Binary Trees

scholarly journals Efficient random sampling of binary and unary-binary trees via holonomic equations

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

scholarly journals The Distribution of Heights of Binary Trees and Other Simple Trees

1993 ◽  
Vol 2 (2) ◽  
pp. 145-156 ◽  
Author(s):  
Philippe Flajolet ◽  
Zhicheng Gao ◽  
Andrew Odlyzko ◽  
Bruce Richmond
Keyword(s):  
Asymptotic Formula ◽  
Positive Constant ◽  
Binary Trees ◽  
Asymptotic Results ◽  
Image Position

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.

scholarly journals On growing random binary trees

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