Combinatorics and Graph Theory

    

Formal Calculation

Authors: Peng Ji

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained many results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry

Comments: 21 Pages.

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Submission history

[v1] 2024-11-07 05:15:59

Unique-IP document downloads: 243 times

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