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We explore the operad of finite posets and its algebras. We use orderpolytopes to investigate the combinatorial properties of zeta values. Bygeneralizing a family of zeta value identities, we demonstrate theapplicability of this approach. In addition, we offer new proofs of some ofRamanujan's results on the properties of Eulerian numbers, interpreting hiswork as dealing with series inheriting the algebraic structure of disjointunions of points. Finally, we establish a connection between our findings andthe linear independence of zeta values.

A poset version of Ramanujan results on Eulerian numbers and zeta values