A Note on Ternary Sequences of Strings of 0 and 1

Abstract

B. D. Acharya has conjectured that if $(A_i:i=1,2,...,2^{|X|}-1)$ is a permutation of all nonempty subsets of a set $X$ with at least two elements such that for each even positive integer $j<2^{|X|}-1$, $A_{j-1}△A_j△A_{j+1}=\varnothing$, then $|X|=2$. In this article, we show that if the cardinality of a set $X$ is more than four, then a permutation as described above indeed exists.

5 pages