On the number of distinct differences in an intersecting family

For a family F of subsets define F \ F = {F \ F' : F, F' is an element of F}. The family F is called intersecting if F boolean AND F' not equal theta for all F, F' is an element of F. We prove best possible upper bounds for vertical bar F \ F vertical bar in the case that F is intersecting. (c) 2020 Elsevier B.V. All rights reserved.