Abstract:In this paper we solve an open problem on distributive lattices, which was proposed by Stanley in 1998. This problem was motivated by a conjecture due to Griggs, which equivalently states that the incomparability graph of the boolean algebra B n is nice. Stanley introduced the idea of studying the nice property of a graph by investigating the Schur positivity of its corresponding chromatic symmetric functions. Since the boolean algebras form a special class of distributive lattices, Stanley raised the question… Show more
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