A note on Möbius inversion over power set lattices
نویسنده
چکیده
In this paper, we establish a theorem on Möbius inversion over power set lattices which strongly generalizes an early result of Whitney on graph colouring.
منابع مشابه
Some Applications of the Möbius Function
The Möbius function is an important concept in combinatorics. First developed for number theory, it has since been extended to arbitrary posets, where it allows inversion of certain functions. One type of poset of particular interest is the subgroup lattice of a finite group. In this paper, we examine some fundamental results about the Möbius function, including the powerful inversion formula, ...
متن کاملA SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS
In this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. It is proved that an abelian group of finite exponent is strongly coatomic.
متن کاملT-Rough Sets Based on the Lattices
The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...
متن کاملA note on approximation conditions, standard triangularizability and a power set topology
The main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. The methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [B. R. Yahaghi, Near triangularizability implies triangularizability, Canad. Math. Bull. 47, (2004), no. 2...
متن کاملGENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM
The aim of the present work is to study the $F$-transform over a generalized residuated lattice. We discuss the properties that are common with the $F$-transform over a residuated lattice. We show that the $F^{uparrow}$-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010