A poset version of Ramanujan results on Eulerian numbers

Eric Dolores-Cuenca

Published 2022-05-10Version 1

We explain how several results of Ramanujan follow from the formalism of order series. Consider the operad generated by a binary associative and commutative operation and a binary associative operation, order series are one of the algebras over this operad. In our interpretation, Ramanujan worked with series inheriting the structure of the disjoint union of posets. We then provide new conceptual proofs of a couple of results by Ramanujan and describe a version of his results that depends on a choice of a series parallel poset.