An improvement on a spernerity proof of Horrocks

In Horrocks' proof (Horrocks, European Journal of Combinatorics 20 (1999) 1 31-148) of Lih's conjecture about the Spernerity of filters in a Boolean al gebra generated by 2-subsets, there are 116 exceptional graphs to be checke d case by case. The details of the analysis could not be published in its e ntirety. In this paper we carry Horrocks' method much further to reduce the exceptional cases to a manageable number. A complete examination can thus be exhibited. (C) 2001 Elsevier Science B.V. All rights reserved.