Uniqueness of linear combinations (mod p)

Hilliker, David Lee; Straus, E. G.

doi:10.1016/0022-314x(86)90052-1

Cited by 1 publication

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for all primes p. Hilliker and Straus [2] studied the following natural generalization of the problem. For a given vectorᾱ = (α 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…First we present a simple argument which shows that in the inequality f (ᾱ, p) ≥ log(p−1) log(2 ᾱ 1 ) + 1, proved by Hilliker and Straus [2], one can replace the factor (log( ᾱ 1 )) −1 by a constant depending only on k.…”

Section: Introductionmentioning

confidence: 99%

“…Proof. Our construction of a set A is a straightforward generalization of the one presented in [2]. Put…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Note on a Problem of Hilliker and Straus

Jańczak¹

2007

Electron. J. Combin.

View full text Add to dashboard Cite

For a prime $p$ and a vector $\bar\alpha=(\alpha_1,\dots,\alpha_k)\in {\Bbb Z}_p^k$ let $f\left(\bar\alpha,p\right)$ be the largest $n$ such that in each set $A\subseteq{\Bbb Z}_{p}$ of $n$ elements one can find $x$ which has a unique representation in the form $x=\alpha_{1}a_1+\dots +\alpha_{k}a_k, a_i\in A$. Hilliker and Straus bounded $f\left(\bar\alpha,p\right)$ from below by an expression which contained the $L_1$-norm of $\bar\alpha$ and asked if there exists a positive constant $c\left(k\right)$ so that $f\left(\bar\alpha,p\right)>c\left(k\right)\log p$. 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 $A\subseteq {\Bbb Z}_{p}$ such that every element of $A+A$ has at least $K$ representations in the form $a+a'$, $a, a'\in A$.

show abstract

“…for all primes p. Hilliker and Straus [2] studied the following natural generalization of the problem. For a given vectorᾱ = (α 1 , .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%