IBM - Personal communication

This web page contains the abstract of my paper:

"A Simple Counterexample to a Conjecture of Rota", Discrete Mathematics, 28(1979), p. 327-330.

Abstract: Consider the poset P(n) of partitions of an n-element set ordered by refinement. Let S(n,k) be the number of partitions containing k blocks. Let L(n) be the maximal length of an antichain in P(n). Rota conjectured that L(n) = max over k of S(n,k). In this paper we construct larger antichains for all n sufficiently large.

[ IBM Research home page | James B. Shearer's home page | Up ]
[ IBM home page | Order | Search | Contact IBM | Help | (C) | (TM) ]