Combinatorics and cluster expansions
نویسندگان
چکیده
منابع مشابه
Combinatorics and cluster expansions
Abstract: This article is about the connection between enumerative combinatorics and equilibrium statistical mechanics. The combinatorics side concerns species of combinatorial structures and the associated exponential generating functions. The passage from species to generating functions is a combinatorial analog of the Fourier transform. Indeed, there is a convolution multiplication on specie...
متن کاملTilting Theory and Cluster Combinatorics
We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field. We show that, in the simply-laced Dynkin case, C can be regarded as a natural model for the combinatorics of the corresponding Fomin–Zelevinsky cluster algebra. In this model, the tilting obj...
متن کاملCombinatorics of cluster enumeration
47 thereby facilitating reduction of polyoxometallates of these types. The concept of binodal orbital aromaticity in reduced early-transition-metal polyoxometallates may be related to their classification as mixed valence compounds. Robin and Day36 classify mixed valence compounds into the following three classes: Class I, fully localized corresponding to an insulator in an infinite system; Cla...
متن کاملCombinatorial Species and Cluster Expansions
This paper will survey recent progress on clarifying the connection between enumerative combinatorics and cluster expansions. The combinatorics side concerns species of combinatorial structures and the associated exponential generating functions. Cluster expansions, on the other hand, are supposed to give convergent expressions for measures on infinite dimensional spaces, such as those that occ...
متن کاملCluster Expansions and Correlation Functions
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecký–Preiss criterion. Expressions and estimates for correlation functions are also presented. The results are applied to systems of interacting classical and quantum particles, and to a lattice polymer model. 2000 Math. Subj. Class. 82B0...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Surveys
سال: 2010
ISSN: 1549-5787
DOI: 10.1214/10-ps159