Word operads and admissible orderings

Abstract

We use Giraudo's construction of combinatorial operads from monoids to offer a conceptual explanation of the origins of Hoffbeck's path sequences of shuffle trees, and use it to define new monomial orders of shuffle trees. One such order is utilised to exhibit a quadratic Gröbner basis of the Poisson operad.

5 pages

Cited by in corpus (8)

• Endofunctors and Poincaré-Birkhoff-Witt theorems
• An effective criterion for Nielsen-Schreier varieties
• Calculus of multilinear differential operators, operator $L_{\infty }$-algebras and ${IBL}_{\infty }$-algebras
• A characterisation of Lie algebras using ideals and subalgebras
• Generalized cohomological field theories in the higher order formalism
• Reconnectads
• Poisson triple systems
• A generalization of operads based on subgraph contractions