Coordinate density of sets of vectors

M. G. Karpovsky, V. D. Milman

Research output: Contribution to journalArticlepeer-review

Abstract

Let no = 0,n1 ≥1...,n3 ≥1 be given natural numbers, Ji= ∑ t=0 0-1ni+1,..., ∑ t=0 tnt (i=Ji,...,s) and Π t=0 s Ena=(x(t),...., x(1): n= ∑ i=1 s n1 and if rε{lunate} Ji, then x(u)ε{lunate}{0,..., qi-J} A set R⊆∏i3 = 1 Eaji2 is said to be (m1, ...,m3)-dense (1≤m1≤n) if there exist I1⊆J1 such that |L1| = m6 (i = 1,...,s) and |L(I)(R)| = ∏I5 = qlm1 where P(I)(R) is the projection of R on the coordinate axes whose indices lie in I = ∪i5 = jL1. In this paper we establish necessary and sufficient conditions for an arbitrary set R⊆∏51 = 1 Ea1n1 with given |R| to be (m1,...,m3)-dense.

Original languageEnglish
Pages (from-to)177-184
Number of pages8
JournalDiscrete Mathematics
Volume24
Issue number2
DOIs
StatePublished - 1978

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