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The Root of a Binomial Coefficient is equal to the Sum of its Leaves

03 October 2022, Version 3
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

This paper focuses on the successive partitions of a binomial coefficient in combinatorial geometric series such as root, predecessor, successor, and leaf of a binomial coefficient. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. These ideas can enable the scientific researchers to solve the real life problems.

Keywords

computation
combinatorics
binomial coefficient
partition method

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Version History

Oct 03, 2022 Version 3

Version Notes

Theorems 2.1 and 3.2 are newly added in the revised version.

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The content is available under CC BY 4.0 [opens in a new tab]

DOI

10.33774/coe-2022-hr86n-v3
D O I: 10.33774/coe-2022-hr86n-v3 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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