On the number of integer points in a multidimensional domain

Autor:	Alexander S. Rybakov
Rok vydání:	2018
Předmět:	010101 applied mathematics Discrete mathematics Applied Mathematics 010102 general mathematics Discrete Mathematics and Combinatorics 0101 mathematics 01 natural sciences Domain (software engineering) Integer (computer science) Mathematics
Zdroj:	Discrete Mathematics and Applications. 28:385-395
ISSN:	1569-3929 0924-9265
Popis:	We provide a new upper estimate for the modulus of the difference |Λ ∩ 𝓢| − voln(𝓢)/det Λ, where 𝓢 ⊂ ℝn is a set of volume voln(𝓢) and Λ ⊂ ℝn is a complete lattice with determinant det Λ. This result has an important practical application, for example, in estimating the number of integer solutions of an arbitrary system of linear and nonlinear inequalities.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::bc5cb2aa2a1edb3bf6415071da2a65b1 https://doi.org/10.1515/dma-2018-0034 Zobrazit plný text záznamu