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The value set of polynomials over ℤ m and the combinatorics of sequences
Author(s) -
Ralph W. J.
Publication year - 1995
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300011487
Subject(s) - mathematics , cardinality (data modeling) , combinatorics , substring , set (abstract data type) , class (philosophy) , order (exchange) , value (mathematics) , discrete mathematics , statistics , finance , artificial intelligence , computer science , economics , data mining , programming language
For a class of functions containing polynomials over ℤ m , we give an inequality relating the cardinality of the value set to the additive order of differences of elements in that set. To do this, we find some inequalities concerning the combinatorics of substrings of sequences on finite sets which are related to an interesting matrix inequality.