 
Summary: ON THE DISCREPANCY
OF COMBINATORIAL RECTANGLES
NOGA ALON, BENJAMIN DOERR, TOMASZ LUCZAK, AND TOMASZ
SCHOEN
Abstract. Let Bd
n denote the family which consists of all subsets
S1 × · · · × Sd, where Si [n], and Si = , for i = 1, . . . , d. We
compute the L2discrepancy of Bd
n and give estimates for the Lp
discrepancy of Bd
n for 1 p .
1. Introduction
For a family of subsets H of a finite set , a colouring :
{1, 1}, and A H, let (A) = aA (a). Then, for 1 p < , we
set
discp(H, ) =
1
H AH
(A)p
1/p
