3-D floorplanning using labeled tree and dual sequences

2008 ◽  
Author(s):  
Renshen Wang ◽  
Evangeline F. Y. Young ◽  
Yi Zhu ◽  
Fan Chung Graham ◽  
Ronald Graham ◽  
...  
Keyword(s):  
Labeled Tree ◽  
Dual Sequences

scholarly journals Congruences related to dual sequences and Catalan numbers

2022 ◽  
Vol 101 ◽  
pp. 103458
Author(s):  
Rong-Hua Wang ◽  
Michael X.X. Zhong
Keyword(s):  
Catalan Numbers ◽  
Dual Sequences

scholarly journals Closed paths whose steps are roots of unity

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Gilbert Labelle ◽  
Annie Lacasse
Keyword(s):  
Roots Of Unity ◽  
Explicit Formulas ◽  
Asymptotic Expressions ◽  
International Audience ◽  
Dual Sequences ◽  
Polygonal Paths

International audience We give explicit formulas for the number $U_n(N)$ of closed polygonal paths of length $N$ (starting from the origin) whose steps are $n^{\textrm{th}}$ roots of unity, as well as asymptotic expressions for these numbers when $N \rightarrow \infty$. We also prove that the sequences $(U_n(N))_{N \geq 0}$ are $P$-recursive for each fixed $n \geq 1$ and leave open the problem of determining the values of $N$ for which the $\textit{dual}$ sequences $(U_n(N))_{n \geq 1}$ are $P$-recursive. Nous donnons des formules explicites pour le nombre $U_n(N)$ de chemins polygonaux fermés de longueur $N$ (débutant à l'origine) dont les pas sont des racines $n$-ièmes de l'unité, ainsi que des expressions asymptotiques pour ces nombres lorsque $N \rightarrow \infty$. Nous démontrons aussi que les suites $(U_n(N))_{N \geq 0}$ sont $P$-récursives pour chaque $n \geq 1$ fixé et laissons ouvert le problème de déterminer les valeurs de $N$ pour lesquelles les suites $\textit{duales}$ $(U_n(N))_{n \geq 1}$ sont $P$-récursives.

scholarly journals The Structure of Locally Finite Two-Connected Graphs

10.37236/1211 ◽  
1995 ◽  
Vol 2 (1) ◽  
Author(s):  
Carl Droms ◽  
Brigitte Servatius ◽  
Herman Servatius
Keyword(s):  
Connected Graph ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Locally Finite ◽  
Connected Graphs ◽  
Finite Graphs ◽  
Locally Finite Graphs ◽  
Necessary And Sufficient ◽  
Block Tree ◽  
Labeled Tree

We expand on Tutte's theory of $3$-blocks for $2$-connected graphs, generalizing it to apply to infinite, locally finite graphs, and giving necessary and sufficient conditions for a labeled tree to be the $3$-block tree of a $2$-connected graph.

scholarly journals Ideals of Numerical Semigroups and Error-Correcting Codes

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1406
Author(s):  
Bras-Amorós
Keyword(s):  
Secret Sharing ◽  
Error Correcting Codes ◽  
Numerical Semigroups ◽  
Secret Sharing Schemes ◽  
List Decoding ◽  
Generalized Hamming Weights ◽  
Resilient Functions ◽  
Weierstrass Semigroups ◽  
Hamming Weights ◽  
Dual Sequences

Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

Structure and Metabolic-Flow Analysis of Molecular Complexity in a 13 C-Labeled Tree by 2D and 3D NMR

2016 ◽  
Vol 55 (20) ◽  
pp. 6000-6003 ◽  
Author(s):  
Takanori Komatsu ◽  
Risa Ohishi ◽  
Amiu Shino ◽  
Jun Kikuchi
Keyword(s):  
Flow Analysis ◽  
3D Nmr ◽  
Molecular Complexity ◽  
2D And 3D ◽  
Labeled Tree

scholarly journals A q-analog of dual sequences with applications

2007 ◽  
Vol 28 (1) ◽  
pp. 214-227 ◽  
Author(s):  
Sharon J.X. Hou ◽  
Jiang Zeng
Keyword(s):  
Dual Sequences
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