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Entropy as a Topological Operad Derivation [PDF]
Entropy, 2021 We share a small connection between information theory, algebra, and topology—namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices.
Tai-Danae Bradley
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An Index for Graphs and Graph Groupoids
Axioms, 2022 In this paper, we consider certain quantities that arise in the images of the so-called graph-tree indexes of graph groupoids. In text, the graph groupoids are induced by connected finite-directed graphs with more than one vertex.
Ilwoo Cho, Palle Jorgensen
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Models for the n‐Swiss Cheese operads
Transactions of the London Mathematical Society, 2021 We describe combinatorial Hopf (co‐)operadic models for the Swiss Cheese operads built from Feynman diagrams. This extends previous work of Kontsevich and Lambrechts‐Volić for the little disks operads.
Thomas Willwacher
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On the non-Koszulity of ternary partially associative operad; pp. 355–363 [PDF]
Proceedings of the Estonian Academy of Sciences, 2010 We prove that the operad for ternary partially associative algebras is non Koszul. The aim is to underline the problem of computing the dual operad when we consider quadratic operad for n-ary algebras in particular when n is odd. In fact, the dual operad
Elisabeth Remm
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Constructing combinatorial operads from monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar combinatorial objects:
Samuele Giraudo
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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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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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