Open AccessPOLYNOMIAL VERSION ON THE SUM-PRODUCT PROBLEM
Author(s) -
Sofia Aleshina,
Il'ya Vladimirovich Vyugin
Publication year - 2020
Publication title -
avtomatizaciâ i modelirovanie v proektirovanii i upravlenii
Language(s) - English
Resource type - Journals
eISSN - 2658-6436
pISSN - 2658-3488
DOI - 10.30987/2658-6436-2020-2-4-10
Subject(s) - mathematics , cardinality (data modeling) , combinatorics , product (mathematics) , generalization , set (abstract data type) , value (mathematics) , polynomial , discrete mathematics , computer science , statistics , mathematical analysis , geometry , data mining , programming language
This work is about the generalization of sum-product problem. The general principle of it was formulated in the Erdos-Szemeredi’s hypothesis. Instead of the Minkowski sum in this hypothesis, the set of values f(x,y) of a homogeneous polynomial f lin two variables, where x and y belong to subgroup G of is considered. The lower bound on the cardinality of such set is obtained. This topic has an applied value in the theory of information and dynamics in calculating the probabilities of events, as well as in various methods of encoding and decoding information.