Some properties of binomial coefficients and their application to growth modelling

Abstract

Some properties of diagonal binomial coefficients were studied in respect to frequency of their units’ digits. An approach was formulated that led to the 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 2n bases. In the work, an application of binomial coefficient arithmetic to model cell population dynamics was suggested. For a multicellular organism, the growth of number of cells was presented as a succession of binomial coefficients. It was inferred that the number of cells in a multicellular organism may obey power function laws.

Keywords

• Binomial coefficients
• natural sequence
• minor total
• multicellular growth