In many areas of mathematics some “higher operations” are arising. These havebecome so
important that several research projects refer to such expressions. Higher operationsform …

This paper provides a general operadic definition for the notion of splitting the operations of
algebraic structures. This construction is proved to be equivalent to some Manin products of …

This book presents a systematic treatment of Grobner bases in several contexts. The book
builds up to the theory of Grobner bases for operads due to the second author and …

We define a new monoidal structure on the category of collections (shuffle composition).
Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of …

We investigate the role that non-crossing partitions play in the study of positroids, a class of
matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely …

Galois explained to us that operations acting on the solutions of algebraic equations are
mathematical objects as well. The notion of an operad was created in order to have a well …

Given a type of algebras there is a notion of “free” algebra over a generic vector space V. Let
us denote it by. Viewed as a functor from the category Vect of vector spaces to itself, is …

We introduce a family of sequence transformations, defined via partial Bell polynomials, that
may be used for a systematic study of a wide variety of problems in enumerative …

In this paper, we introduce cell-forms on 𝔐0, n, which are top-dimensional differential forms
diverging along the boundary of exactly one cell (connected component) of the real moduli …

We show how to use Groebner bases for operads to prove various freeness theorems:
freeness of certain operads as nonsymmetric operads, freeness of an operad Q as a P …