Finitary bases and formal generating functions
نویسندگان
چکیده
Let k be a nonzero, commutative ring with 1, and let R be a k-algebra with a countably-infinite ordered free k-basis B = {pn: n~>0}. We characterize and analyze those bases from which one can construct a k-algebra of 'formal B-series' of the form f = ~ c , p , , with cn Ek, showing inter alia that many classical polynomial bases fail to have this property. @ 1998 Elsevier Science B.V. All rights reserved
منابع مشابه
On composition of generating functions
In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...
متن کاملA Note on the Axioms for Zilber's Pseudo-Exponential Fields
We show that Zilber’s conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the firstorder types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-or...
متن کاملFinitary formal topologies and Stone's representation theorem
We study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theo...
متن کاملAbteilung Wissensbasierte Systeme Reasoning about Evolving Nonmonotonic Knowledge Bases
Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which use an update policy for specifying how updates must be incorporated. In this paper, we introduce a framework for reasoning about evolving knowledge bases, wh...
متن کاملAn Algebraic Approach to Energy Problems I - *-Continuous Kleene ω-Algebras
Energy problems are important in the formal analysis of embedded or autonomous systems. With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Motivated by this application and in order to compute ...
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:
- Discrete Mathematics
دوره 190 شماره
صفحات -
تاریخ انتشار 1998