On subtrees of the representation tree in rational base numeration systems
نویسندگان
چکیده
Every rational number p q defines a rational base numeration system in which every integer has a unique finite representation, up to leading zeroes. This work is a contribution to the study of the set of the representations of integers. This prefix-closed subset of the free monoid is naturally represented as a highly non-regular tree. Its nodes are the integers, its edges bear labels taken in {0, 1, . . . , p− 1}, and its subtrees are all distinct.
منابع مشابه
On the cost and complexity of the successor function
For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word of a genealogically ordered language L onto the (n+1)-th word of L. We show that, if the ratio of the number of elements of length n+ 1 over the number of elements of length n of the language h...
متن کاملThe signature of rational languages
We present here the notion of signature of trees and of languages, and its relationships with the theory of numeration systems. The signature of an ordered infinite tree (of bounded degree) is an infinite (bounded) sequence of integers, the sequence of the degrees of the nodes taken in the visit order of the canonical breadth-first traversal of the tree. A prefix-closed language defines such a ...
متن کاملTrees and Languages with Periodic Signature
The signature of a labelled tree (and hence of its prefix-closed branch language) is the sequence of the degrees of the nodes of the tree in the breadth-first traversal. In a previous work, we have characterised the signatures of the regular languages. Here, the trees and languages that have the simplest possible signatures, namely the periodic ones, are characterised as the sets of representat...
متن کاملRepresenting real numbers in a generalized numeration system
numeration systems An abstract numeration system (ANS) is given by a triplet S = (L,Σ, <) where L is a regular language over a totally ordered alphabet (Σ, <). By enumerating the words in L with respect to the radix order induced by <, we define a one-to-one correspondence: repS : N → L valS = rep −1 S : L → N. ANS: a generalization Most numeration systems satisfy the relation: m < n (usual ord...
متن کاملRepresenting Real Numbers in a Generalized Numeration Systems
We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show that our framework can be applied to the rational base numeration systems.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 20 شماره
صفحات -
تاریخ انتشار 2018