Use of difference tables at studying of properties of binomial coefficients

Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of binomial coefficients at quadratic terms of the binomial theore...

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Bibliographic Details
Published in:arXiv.org 2017-04
Main Author: Gavrikov, Vladimir L
Format: Article
Language:English
Subjects:
Binomial coefficients
Binomial theorem
Digits
Numbering schemes
Online Access:Get full text
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Summary:Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of binomial coefficients at quadratic terms of the binomial theorem. Frequency distributions of units digits of binomial coefficients contain gaps (zero frequency) under most common numbering systems with supposed exclusion to systems with 2^n bases. Binomial coefficient arithmetics may be used to model cell population dynamics in a multicellular organism, which implies that the dynamics obeys power function laws.
ISSN:2331-8422