3 papers
math.QA2025
Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets
Paul Laubie
We show a variation of the usual homological freeness criterion for operadic modules over a Koszul operad. We then apply this result to decorated partition posets for some operads,…
math.QA2025
On Hilbert series of Koszul operads and a classification result for set-operads
Paul Laubie
Motivated by numerous examples in the literature, we state a conjecture on the Hilbert series of Koszul symmetric operads generated by one element of arity . We prove this conje…
math.NA2025
Elementary differentials from multi-indices to rooted trees
Yvain Bruned, Paul Laubie
Rooted trees are essential for describing numerical schemes via the so-called B-series. They have also been used extensively in rough analysis for expanding solutions of singular S…