Characterization of rational and algebraic power series
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 کاملALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)
We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
متن کاملALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)
We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
متن کاملAxiomatizing rational power series
Iteration semirings are Conway semirings satisfying Conway’s group identities. We show that the semirings Nrat〈〈Σ∗〉〉 of rational power series with coefficients in the semiring N of natural numbers are the free partial iteration semirings. Moreover, we characterize the semirings Nrat ∞ 〈〈Σ∗〉〉 as the free semirings in the variety of iteration semirings defined by three additional simple identitie...
متن کاملRational and algebraic series in combinatorial enumeration
Let A be a class of objects, equipped with an integer size such that for all n the number an of objects of size n is finite. We are interested in the case where the generating function ∑ n ant n is rational, or more generally algebraic. This property has a practical interest, since one can usually say a lot on the numbers an, but also a combinatorial one: the rational or algebraic nature of the...
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: RAIRO. Informatique théorique
سال: 1983
ISSN: 0399-0540
DOI: 10.1051/ita/1983170100031