Access Restriction

Author Janczak, Mirosława
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract For a prime p and a vector ¯α = (α1,..., αk) ∈ Z k p let f (¯α, p) be the largest n such that in each set A ⊆ Zp of n elements one can find x which has a unique representation in the form x = α1a1 + · · · + αkak, ai ∈ A. Hilliker and Straus [2] bounded f (¯α, p) from below by an expression which contained the L1-norm of ¯α and asked if there exists a positive constant c (k) so that f (¯α, p)> c (k) log p. In this note we answer their question in the affirmative and show that, for large k, one can take c(k) = O(1/k log(2k)). We also give a lower bound for the size of a set A ⊆ Zp such that every element of A + A has at least K representations in the form a + a ′ , a, a ′ ∈ A.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Publisher Date 2007-01-01