Numbers of solutions of linear diophantine equations and their applications in the theory of invariant cubature formulas

1981 ◽  
Vol 22 (2) ◽  
pp. 260-273
Author(s):  
M. I. Israilov
Keyword(s):  
Diophantine Equations ◽  
Cubature Formulas ◽  
Linear Diophantine Equations ◽  
Invariant Cubature Formulas

Coordination sequences and layer-by-layer growth of periodic structures

2019 ◽  
Vol 234 (5) ◽  
pp. 291-299
Author(s):  
Anton Shutov ◽  
Andrey Maleev
Keyword(s):  
Generating Functions ◽  
Diophantine Equations ◽  
Periodic Structures ◽  
Layer Growth ◽  
Layer By Layer ◽  
Explicit Formulas ◽  
New Approach ◽  
Coordination Numbers ◽  
Linear Diophantine Equations ◽  
Recurrent Relations

Abstract A new approach to the problem of coordination sequences of periodic structures is proposed. It is based on the concept of layer-by-layer growth and on the study of geodesics in periodic graphs. We represent coordination numbers as sums of so called sector coordination numbers arising from the growth polygon of the graph. In each sector we obtain a canonical form of the geodesic chains and reduce the calculation of the sector coordination numbers to solution of the linear Diophantine equations. The approach is illustrated by the example of the 2-homogeneous kra graph. We obtain three alternative descriptions of the coordination sequences: explicit formulas, generating functions and recurrent relations.

scholarly journals On the Non-Linear Diophantine Equations 31x + 41y = z2 and 61x + 71y = z2

2018 ◽  
Vol 18 (2) ◽  
pp. 185-188
Author(s):  
Satish Kumar ◽  
◽  
Deepak Gupta ◽  
Hari Kishan
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations ◽  
Non Linear

scholarly journals Semigroup ideals and linear diophantine equations

1999 ◽  
Vol 295 (1-3) ◽  
pp. 133-144 ◽  
Author(s):  
A. Vigneron-Tenorio
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations

Geometrical Regular Languages and Linear Diophantine Equations

2011 ◽  
pp. 107-120 ◽  
Author(s):  
Jean-Marc Champarnaud ◽  
Jean-Philippe Dubernard ◽  
Franck Guingne ◽  
Hadrien Jeanne
Keyword(s):  
Diophantine Equations ◽  
Regular Languages ◽  
Linear Diophantine Equations

Few Non-Linear Diophantine Equations

2021 ◽  
pp. 295-306
Author(s):  
Satyabrota Kundu ◽  
Sypriyo Mazumder
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations ◽  
Non Linear

Jacobi's Solution of Linear Diophantine Equations

1975 ◽  
Vol 48 (3) ◽  
pp. 159-163
Author(s):  
M. S. Waterman
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations
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