 
Summary: JOURNAL OF COMBINATORIAL THEORY, Series B 47, 153161 (1989)
Combinatorial Reconstruction Problems
N. ALON*, Y. CARO, I. KRASIKOV, AND Y. RODITTY
School of Mathematical Sciences,
Raymond and Beverley Sackler Faculty of Exact Sciences,
TelAviv University, TelAviv, Israel
Communicated by the Editors
Received February 4, 1987
A general technique for tackling various reconstruction problems is presented
and applied to some old and some new instances of such problems. 0 1989 Academic
Press, Inc.
1. INTRODUCTION
Let X be a (finite or infinite) set and let G be a (finite or infinite) group
of automorphisms of X. Thus G acts on X and for every g EG the sequence
k&x is a permutation of X. For every subset Y of X and every g E G,
let g Y be the set of all elements gy, for y E Y. Clearly 1g Y 1= 1Y 1for every
finite Y, and this defines an action of the group G on the power set of X.
The orbit of a subset Y of X is, as usual, the set YG= {g Y: g E G}. We say
that two subsets Y and 2 of X are Gequivalent iff there is an element g of
the group G mapping Y into 2, i.e., iff ZE p. Let R be a set of repre
