Nonabelian Sets with Distinct k -sums


A.M. Odlyzko, AT&T Bell Laboratories;W.D. Smith, NECII

02/10/93

ABSTRACT:
A modified Bose-Chowla construction of sets with distinct sums of
$k$-element subsets is presented. In infinitely many cases it yields sets
with a certain multiplicative symmetry. These sets are then used to
construct large sets $S$ in certain nonabelian groups with the property
that all $k$-letter words with letters from $S$ are distinct.


  KEYWORDS:
$S_K$-SETS, SETS WITH DISTINCT SUMS, ADDITIVE BASIS,
GROUPS, COMBINATORICS