The Art of Computer Programming, Volume 4, Fascicle 5: Mathematical Preliminaries Redux; Introduction to Backtracking; Dancing Links

76. (a) Eliminate the n items for xx; use only the options of type (iii) for which y ≠ z. (Idempotent gropes are equivalent to “Mendelsohn triples,” which are families of n(n − 1)/3 three-cycles (xyz) that include every ordered pair of distinct elements. N. S. Mendelsohn proved [Computers in Number Theory (New York: Academic Press, 1971), 323–338] that such systems exist for all n ≢ 2 (modulo 3), except when n = 6.

(b) Use only the items xy for 0 ≤ x ≤ y < n; replace options of type (ii) by ‘xx xy’ and ‘xy yy’ for 0 ≤ x < y < n; replace those ...