Operated semigroups, Motzkin paths and rooted trees
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Publication:1016141
DOI10.1007/s10801-007-0119-7zbMath1227.05271arXiv0710.0429OpenAlexW2165487201MaRDI QIDQ1016141
Publication date: 4 May 2009
Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0710.0429
Related Items (57)
Free involutive Hom-semigroups and Hom-associative algebras ⋮ Hopf algebra structure on free Rota-Baxter algebras by angularly decorated rooted trees ⋮ Rota's classification problem, rewriting systems and Gröbner-Shirshov bases ⋮ Hopf algebra of multidecorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases ⋮ Extensions of operators, liftings of monads, and distributive laws ⋮ Averaging algebras, rewriting systems and Gröbner–Shirshov bases ⋮ Dendriform-Nijenhuis bialgebras and DN-associative Yang-Baxter equations ⋮ Rota-Baxter operators on Turaev's Hopf group (co)algebras. I: Basic definitions and related algebraic structures ⋮ Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras ⋮ Hopf algebras of planar binary trees: an operated algebra approach ⋮ Diassociative family algebras and averaging family operators ⋮ Rota–Baxter family Ω-associative conformal algebras and their cohomology theory ⋮ Averaging algebras, Schröder numbers, rooted trees and operads ⋮ Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects ⋮ Construction of free commutative Reynolds algebras by Gröbner-Shirshov bases ⋮ Free weighted (modified) differential algebras, free (modified) Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases ⋮ Locality and renormalization: Universal properties and integrals on trees ⋮ Free Rota-Baxter family algebras and free (tri)dendriform family algebras ⋮ Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems ⋮ Typed angularly decorated planar rooted trees and generalized Rota-Baxter algebras ⋮ λ-TD algebras, generalized shuffle products and left counital Hopf algebras ⋮ Rota-Baxter TD Algebra and Quinquedendriform Algebra ⋮ On rings of differential Rota–Baxter operators ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Classification of operator extensions, monad liftings and distributive laws for differential algebras and Rota–Baxter algebras ⋮ Rota-Baxter algebras and dendriform algebras. ⋮ Rota-Baxter modules toward derived functors ⋮ Free integro-differential algebras and Gröbner-Shirshov bases. ⋮ Relative locations of subwords in free operated semigroups and Motzkin words. ⋮ Constructions of Free Commutative Integro-Differential Algebras ⋮ Free operated monoids and rewriting systems ⋮ CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES ⋮ Enumeration and generating functions of Rota-Baxter words. ⋮ Enumeration and generating functions of differential Rota-Baxter words. ⋮ Universal enveloping algebras and Poincar\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras ⋮ Left counital Hopf algebras on free Nijenhuis algebras ⋮ Free (tri)dendriform family algebras ⋮ Free objects and Gröbner-Shirshov bases in operated contexts ⋮ Weighted infinitesimal unitary bialgebras of rooted forests, symmetric cocycles and pre-Lie algebras ⋮ Braided dendriform and tridendriform algebras, and braided Hopf algebras of rooted trees ⋮ Reynolds algebras and their free objects from bracketed words and rooted trees ⋮ Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras ⋮ Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Free nonunitary Rota-Baxter family algebras and typed leaf-spaced decorated planar rooted forests ⋮ Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras ⋮ Free Rota-Baxter family algebras and (tri)dendriform family algebras ⋮ Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles ⋮ Infinitesimal unitary Hopf algebras and planar rooted forests ⋮ An algebraic study of Volterra integral equations and their operator linearity ⋮ Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras ⋮ Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras. ⋮ A new classification of algebraic identities for linear operators on associative algebras ⋮ Twisted Rota-Baxter families and NS-family algebras ⋮ Dendriform algebras relative to a semigroup ⋮ Double shuffle relations for arborified zeta values
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