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arXiv · 2203.03023

Symmetric functions and a natural framework for combinatorial and number theoretic sequences

Cormac O'Sullivan
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Abstract

Certain triples of power series, considered by I. Macdonald, give a natural framework for many combinatorial and number theoretic sequences, such as the Stirling, Bernoulli and harmonic numbers and partitions of different kinds. The power series in such a triple are closely linked by identities coming from the theory of symmetric functions. We extend the work of Z-H. Sun, who developed similar ideas, and Macdonald, revealing more of the structure of these triples. De Moivre polynomials play a key role in this study.

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Cormac O'Sullivan. 2022-03-06. Symmetric functions and a natural framework for combinatorial and number theoretic sequences. https://arxiv.org/abs/2203.03023

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