Kavli Affiliate: Jing Wang
| First 5 Authors: Jing Wang, Jing Wang, , ,
| Summary:
Let $G$ be a finite abelian group of order $n$, and for each $ain G$ and
integer $1le hle n$ let $mathcalF_a(h)$ denote the family of all
$h$-element subsets of $G$ whose sum is $a$. A problem posed by Katona and
Makar-Limanov is to determine whether the minimum and maximum sizes of the
families $mathcalF_a(h)$ (as $a$ ranges over $G$) become asymptotically
equal as $nrightarrow infty$ when $h=leftlfloorfracn2rightrfloor$.
We affirmatively answer this question and in fact show that the same asymptotic
equality holds for every $4leq hleq leftlfloorfracn2rightrfloor+1$.
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