Results 11 to 20 of about 120 (113)
Logical Methods in Computer Science, 2015 An operad (this paper deals with non-symmetric operads)may be conceived as a partial algebra with a family of insertion operations, Gerstenhaber's circle-i products, which satisfy two kinds of associativity, one of them involving commutativity.
Kosta DOSEN, Zoran Petric
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Redfield-Pólya theorem in $\mathrm{WSym}$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give noncommutative versions of the Redfield-Pólya theorem in $\mathrm{WSym}$, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras.
Jean-Paul Bultel +3 more
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Splitting of Operads and Rota-Baxter Operators on Operads [PDF]
Applied Categorical Structures, 2016 This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendriform algebra of Loday that splits the associative operation to the successors that split any binary operad.
Jun Pei, Chengming Bai, Li Guo 0003
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A bijection between shrubs and series-parallel posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Motivated by the theory of operads, we introduce new combinatorial objects, called shrubs, that generalize forests of rooted trees. We show that the species of shrubs is isomorphic to the species of series-parallel posets.
Frédéric Chapoton
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Discrete Mathematics & Theoretical Computer Science, 2013 In this extended abstract we consider the poset of weighted partitions Π _n^w, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads.
Rafael González S. D'León +1 more
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The Discrete Fundamental Group of the Associahedron [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras.
Christopher Severs, Jacob White
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Formal Lagrangian Operad [PDF]
International Journal of Mathematics and Mathematical Sciences, 2010 Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of the Lagrangian submanifolds of via symplectic reduction. If M is also a symplectic groupoid, then its multiplication space is an associative product in this operad.
Alberto S. Cattaneo +2 more
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The Alternative Operad Is Not Koszul [PDF]
Experimental Mathematics, 2011 v3: added ...
Askar Dzhumadil'daev, Pasha Zusmanovich
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Category-colored Operads, Internal Operads, and Markl $\mathbb{O}$-operads
, 2023 We present a Markl-style definition of operads colored by a small category. In the presence of a unit these are equivalent to substitudes of Day and Street. We show that operads colored by a category are internal algebras of a certain categorical operad of functors.
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$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures [PDF]
Categories and General Algebraic Structures with Applications, 2015 In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads.
Camell Kachour
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