Supersolvable lattices
Supersolvable lattices
复制标题
DOI：
10.1007/bf02945028
复制
发表时间：
1972
影响因子：
0.6
通讯作者：
R. Stanley
中科院分区：
文献类型：
--
作者：
R. Stanley
我们将研究一类有限格，我们称之为超可解格(原因稍后将阐明)。这些格L具有许多有趣的组合性质，这些性质与L中链的计数有关，这些性质可以用Mtibius函数来表示。我感谢裁判的有益建议，这些建议用更简单的证据得出了更一般的结果。定义。设L是有限格，A是L的极大链，如果对L的任一链K，K和A生成的子格都是分配的，则称A为L的M-链；我们称(L，A)为超可解格(或SS-格)。有时，由于滥用记号，我们将L本身称为SS-格，默许为M-链A。
We shall investigate a certain class of finite lattices which we call supersolvable lattices (for a reason to be made clear shortly). These lattices L have a number of interesting combinatorial properties connected with the counting of chains in L, which can be formulated in terms of Mtibius functions. I am grateful to the referee for his helpful suggestions, which have led to more general results with simpler proofs.1.1. DEFINITION. Let L be a finite lattice and A a maximal chain of L. If, for every chain K of L, the sublattice generated by K and A is distributive, then we call A an M-chain of L; and we call (L, A) a supersolvable lattice (or SS-lattice). Sometimes, by abuse of notation, we refer to L itself as an SS-lattice, the M-chain A being tacitly assumed.