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EXPANDERS ON MATRICES OVER A FINITE CHAIN RING, II.
- Source :
-
SIAM Journal on Discrete Mathematics . 2023, Vol. 37 Issue 3, p1587-1609. 23p. - Publication Year :
- 2023
-
Abstract
- This work is a continuation of our previous work [D. M. Ha and H. T. Ngo. Int. J. Math., 34 (2023)], studying the expanding phenomenon in matrices over a finite chain ring with large residue field. A sum-product estimate is proved. It is shown that xy+z+t is a very strong expander, and that x(y + z) and xyz + x are moderate expanders of exponent 13. These results generalize the works of Le and Nguyen (see [J. Number. Theory, 216 (2020), pp. 174--191] and [Discrete Appl. Math., 322 (2022), pp. 166--170]. The solvability in large subsets of the equation xy = z + t is obtained, providing an answer to a question raised by Gyarmati and S\'ark\"ozy [Acta Math. Hungar., 119 (2008), pp. 259--280]. The proofs use spectral graph theory and elementary divisor theory. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE rings
*DIVISOR theory
*GRAPH theory
*MATHEMATICS
*EXPONENTS
Subjects
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 37
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 173328533
- Full Text :
- https://doi.org/10.1137/22M1514362