# General numeration I. Gauged schemes.

• Volume: 42, Issue: 1-2-3, page 38-50
• ISSN: 0373-0999

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## Abstract

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The paper deals with special partitions of whole numbers in the following form: given a sequence of pairs {[Gi;Di]} of positive integers in which the Gi form a strictly increasing sequence, sums of the form ∑niGi, with 0 ≤ ni ≤ Di, are considered. The correspondence[nk ... n0] → ∑i≤k niGidefines then a mapping α from a set M of numerals, called Neugebauer symbols, satisfying 0 ≤ ni ≤ Di, into the set W of all non-negative integers. In M, initial zeros are supressed and M is ordered in the usual numerical order. Such an α is called a gauged scheme.

## How to cite

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Dubois, D. W.. "General numeration I. Gauged schemes.." Revista Matemática Hispanoamericana 42.1-2-3 (1982): 38-50. <http://eudml.org/doc/39825>.

@article{Dubois1982,
abstract = {The paper deals with special partitions of whole numbers in the following form: given a sequence of pairs \{[Gi;Di]\} of positive integers in which the Gi form a strictly increasing sequence, sums of the form ∑niGi, with 0 ≤ ni ≤ Di, are considered. The correspondence[nk ... n0] → ∑i≤k niGidefines then a mapping α from a set M of numerals, called Neugebauer symbols, satisfying 0 ≤ ni ≤ Di, into the set W of all non-negative integers. In M, initial zeros are supressed and M is ordered in the usual numerical order. Such an α is called a gauged scheme.},
author = {Dubois, D. W.},
journal = {Revista Matemática Hispanoamericana},
keywords = {Esquemas calibradores; Sistemas de numeración; gauged scheme},
language = {eng},
number = {1-2-3},
pages = {38-50},
title = {General numeration I. Gauged schemes.},
url = {http://eudml.org/doc/39825},
volume = {42},
year = {1982},
}

TY - JOUR
AU - Dubois, D. W.
TI - General numeration I. Gauged schemes.
JO - Revista Matemática Hispanoamericana
PY - 1982
VL - 42
IS - 1-2-3
SP - 38
EP - 50
AB - The paper deals with special partitions of whole numbers in the following form: given a sequence of pairs {[Gi;Di]} of positive integers in which the Gi form a strictly increasing sequence, sums of the form ∑niGi, with 0 ≤ ni ≤ Di, are considered. The correspondence[nk ... n0] → ∑i≤k niGidefines then a mapping α from a set M of numerals, called Neugebauer symbols, satisfying 0 ≤ ni ≤ Di, into the set W of all non-negative integers. In M, initial zeros are supressed and M is ordered in the usual numerical order. Such an α is called a gauged scheme.
LA - eng
KW - Esquemas calibradores; Sistemas de numeración; gauged scheme
UR - http://eudml.org/doc/39825
ER -

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