Quotients of the magmatic operad: lattice structures and convergent rewrite systems
| Autor: | Samuele Giraudo, Cyrille Chenavier, Christophe Cordero |
|---|---|
| Přispěvatelé: | Laboratoire d'Informatique Gaspard-Monge (LIGM), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
18D50 68Q42 05C05 General Mathematics Rewrite rule Binary number 0102 computer and information sciences Crystal structure 01 natural sciences Mathematics::Algebraic Topology Set (abstract data type) Mathematics::K-Theory and Homology Mathematics::Quantum Algebra Mathematics::Category Theory [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Mathematics - Combinatorics 0101 mathematics Quotient Mathematics 010102 general mathematics Lattice (module) 010201 computation theory & mathematics [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] Combinatorics (math.CO) Tree (set theory) Generator (mathematics) |
| Zdroj: | Experimental Mathematics Experimental Mathematics, Taylor & Francis, 2019, ⟨10.1080/10586458.2019.1577768⟩ |
| ISSN: | 1058-6458 |
| Popis: | We study quotients of the magmatic operad, that is the free nonsymmetric operad over one binary generator. In the linear setting, we show that the set of these quotients admits a lattice structure and we show an analog of the Grassmann formula for the dimensions of these operads. In the nonlinear setting, we define comb associative operads, that are operads indexed by nonnegative integers generalizing the associative operad. We show that the set of comb associative operads admits a lattice structure, isomorphic to the lattice of nonnegative integers equipped with the division order. Driven by computer experimentations, we provide a finite convergent presentation for the comb associative operad in correspondence with~$3$. Finally, we study quotients of the magmatic operad by one cubic relation by expressing their Hilbert series and providing combinatorial realizations. 30 pages |
| Databáze: | OpenAIRE |
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