Non-commutative Rational Power Series and Algebraic Generating Functions
نویسندگان
چکیده
منابع مشابه
Non-commutative Rational Power Series and Algebraic Generating Functions
Sequences of numbers abound in combinatorics whose generating functions are algebraic over the rational functions. Examples include Catalan and related numbers, numbers of words expressing an element in a free group, and diagonal coe cients of 2-variable rational generating functions (Furstenberg's theorem). Algebraicity is of of practical as well as theoretical interest, since it guarantees an...
متن کاملMatrix-J-unitary Non-commutative Rational Formal Power Series
Formal power series in N non-commuting indeterminates can be considered as a counterpart of functions of one variable holomorphic at 0, and some of their properties are described in terms of coefficients. However, really fruitful analysis begins when one considers for them evaluations on N-tuples of n× n matrices (with n = 1, 2, . . .) or operators on an infinite-dimensional separable Hilbert s...
متن کاملThe special subgroup of invertible non-commutative rational power series as a metric group
1: We give an easy proof of Schützenberger’s Theorem stating that non-commutative formal power series are rational if and only if they are recognisable. A byproduct of this proof is a natural metric on a subgroup of invertible rational non-commutative power series. We describe a few features of this metric group.
متن کاملNon-commutative Algebraic Geometry
0 Introduction This is a reasonably faithful account of the ve lectures I delivered at the summer course \Geometria Algebraica no Commutativa y Espacios Cuanti-cos" for graduate students, in Spain, July 25{29, 1994. The material covered was, for the most part, an abridged version of Artin and Zhang's paper 2]. Fix a eld k. Given a Z-graded k-algebra, A say, which for simplicity is assumed to be...
متن کاملNon Recursive Functions Have Transcendental Generating Series
In this note we shaii prove that non primitive recursive functions have transcendental generating series. This resuit translates a certain measure of the complexity of a fonction, the fact of not being primitive recursive, into another measure of the complexity of the generating series associated to the function, the fact of being transcendental. Résumé. On démontre que les fonctions qui ne son...
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: European Journal of Combinatorics
سال: 1993
ISSN: 0195-6698
DOI: 10.1006/eujc.1993.1036