A poset version of Ramanujan results on Eulerian numbers and zeta values
Combinatorics
2023-05-01 v3 Number Theory
Abstract
We explore the operad of finite posets and its algebras. We use order polytopes to investigate the combinatorial properties of zeta values. By generalizing a family of zeta value identities, we demonstrate the applicability of this approach. In addition, we offer new proofs of some of Ramanujan's results on the properties of Eulerian numbers, interpreting his work as dealing with series inheriting the algebraic structure of disjoint unions of points. Finally, we establish a connection between our findings and the linear independence of zeta values.
Keywords
Cite
@article{arxiv.2205.05208,
title = {A poset version of Ramanujan results on Eulerian numbers and zeta values},
author = {Eric Dolores-Cuenca and Jose L. Mendoza-Cortes},
journal= {arXiv preprint arXiv:2205.05208},
year = {2023}
}
Comments
We discovered how to generalize our results to arbitrary finite posets. We explain the relationship between our work and linear independence of zeta values