IJPAM: Volume 78, No. 8 (2012)

WHAT'S IN A BARCODES?: DUPLICATED COMBINATIONS

Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN


Abstract. This article explains how barcodes are read mathematically. One numeral is constructed from 7 modules in a barcode. Firstly, a counting method is presented through which the number of different characters which can be expressed is obtained. After touching upon formulae for permutations and combinations, duplicated combinations are expressed explicitly. The use of a modulus of 10 is mentioned with regard to the calculation of check digits.

Received: March 5, 2012

AMS Subject Classification: 00A09, 90C08, 97A20

Key Words and Phrases: barcode, tree diagram, permutation, combination, duplicated permutation, duplicated combination, check digits, modulo 10

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 8