منابع مشابه
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Stanley [18] introduced the notion of a supersolvable lattice, L, in part to combinatorially explain the factorization of its characteristic polynomial over the integers when L is also semimodular. He did this by showing that the roots of the polynomial count certain sets of atoms of the lattice. In the present work we define an object called an atom decision tree. The class of semimodular latt...
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Abstract. We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [MT] by combining results of McNamara [Mc] and Liu [Li]. As part of our proof, we show that the maximum graded quotient of the free product of a chain and a single-element lattice is finite and di...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.03.005