Modular elements of higher-weight dowling lattices
نویسندگان
چکیده
منابع مشابه
Modular Elements of Geometric Lattices
Let L be a finite geometric lattice of rank n with rank function r. (For definitions, see e.g., [3, Chapter 2], [4], or [1, Chapter 4].) An element x s L is called a modular element if it forms a modular pair with every y e L , i.e., if a<~y then a V ( x A y ) = (a v x )Ay . Recall that in an upper semimodular lattice (and thus in a geometric lattice) the relation of being a modular pair is sym...
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Left-modularity is a concept that generalizes the notion of modularity in lattice theory. In this paper, we give a characterization of left-modular elements and derive two formulae for the characteristic polynomial, /, of a lattice with such an element, one of which generalizes Stanley's theorem [6] about the partial factorization of / in a geometric lattice. Both formulae provide us with induc...
متن کاملThe Generalized Dowling Lattices
In this paper we study a new class of lattices called the generalized Dowling lattices. These lattices are parametrized by a positive integer n , a finite group G , and a meet sublattice K of the lattice of subgroups of G . For an appropriate choice of K the generalized Dowling lattice Dn{G,K) agrees with the ordinary Dowling lattice Dn(G). For a different choice of K, the generalized Dowling l...
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Dowling lattices and their generalizations introduced by Hanlon are interpreted as lattices of congruences associated to certain quasi-varieties of sets with group actions. This interpretation leads, by a simple application of Mobius inversion, to polynomial identities which specialize to Hanlon's evaluation of the characteristic polynomials of generalized Dowling lattices. Analogous results ar...
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Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice Qn(G) (Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions Qn(G) which was recently introduced by Hultman (http://www.math.kth.se/ ~hultman/, 2006), together with the complex of G-symmetric phylogenetic trees T G n . Hult...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90113-8