arXiv subjects

Jovana Obradović

Publications and source records attributed to Jovana Obradović.

8 recordsLinked to original sources

arXiv2026

Generalised flip order on the faces of nestohedra

Classical shuffle products on permutations and binary planar rooted trees (i.e., on the vertices of permutohedra and associahedra) admit descriptions in terms of intervals in the weak Bruhat order and the Tamari order, respectively. Palacios and Ronco extended these products as well as their interval description to surjections and planar rooted trees (i.e. on all faces of permutohedra and associahedra). In this article, we present a broad generalisation of this phenomenon. We show that the shuffle product on faces of certain families of nestohedra admits an interval description with respect to the generalised flip order, a partial order defined on the faces of nestohedra through elementary splitting and fusion operations on the tree-like combinatorial objects encoding them. The generalised flip order extends the flip order of Barnard and McConville from vertices to all faces of nesthedra. We further compare it with the facial weak order of Dermenjian-Hohlweg-Pilaud and the generalised Tamari order of Ronco, and we provide its characterisation in terms of (generalised) inversions.

math.CO↗

arXiv2026

Tridendriform algebras on hypergraph polytopes, the other way around

Hypergraph polytopes (or nestohedra) form a broad class of polytopes obtained by truncating faces of a simplex according to a hypergraph. In earlier work, the authors constructed q-tridendriform algebras on the set of faces of certain families of hypergraph polytopes, including associahedra and permutohedra. The well-definedness of these structures relied on a connectedness property on the hypergraphs involved, called strictness. Nevertheless, notable examples of hypergraph polytopes such as cyclohedra fell outside this setting. We introduce a new connectedness condition, called anti-strictness, which goes opposite to strictness and captures a different class of hypergraph polytopes, including associahedra, permutohedra and cyclohedra. Our main result produces natural (-1)-tridendriform algebras in the anti-strict framework, which match previously introduced tridendriform algebras in the overlap of the two frameworks, thereby extending the range of hypergraph polytopes admitting such algebraic structures.

math.CO↗

arXiv2026

The Bénabou-Roubaud theorem via string diagrams

We give a complete proof of the Bénabou-Roubaud monadic descent theorem using the graphical calculus of string diagrams. Our proof links the monadic and Grothendieck's original viewpoint on descent via an internal-category-based characterization of the category of descent data, equivalent to the one of Janelidze and Tholen.

math.CT↗

arXiv2022

Minimal models for graph-related (hyper)operads

We construct explicit minimal models for the (hyper)operads governing modular, cyclic and ordinary operads, and wheeled properads, respectively. Algebras for these models are homotopy versions of the corresponding structures.

math.CT↗

arXiv2022

Tridendriform algebras on hypergraph polytopes

We extend the works of Loday-Ronco and Burgunder-Ronco on the tridendriform decomposition of the shuffle product on the faces of associahedra and permutohedra, to other families of hypergraph polytopes (or nestohedra), including simplices, hypercubes and some new families. We also extend the shuffle product to take more than two arguments, and define accordingly a new algebraic structure, that we call polydendriform, from which the original tridendriform equations can be crisply synthesized.

math.CO↗

arXiv2019

Combinatorial homotopy theory for operads

We introduce an explicit combinatorial characterization of the minimal model ${\cal O}_{\infty}$ of the coloured operad ${\cal O}$ encoding non-symmetric operads. In our description of ${\cal O}_{\infty}$, the spaces of operations are defined in terms of hypergraph polytopes and the composition structure generalizes the one of the $A_{\infty}$-operad. As further generalizations of this construction, we present a combinatorial description of the $W$-construction applied on ${\cal O}$, as well as of the minimal model of the coloured operad ${\cal C}$ encoding non-symmetric cyclic operads.

math.AT↗

arXiv2017

A formal language for cyclic operads

We propose a $λ$-calculus-style formal language, called the $μ$-syntax, as a lightweight representation of the structure of cyclic operads. We illustrate the rewriting methods behind the formalism by giving a complete step-by-step proof of the equivalence between the unbiased and biased definitions of cyclic operads.

math.AT↗

arXiv2017

Monoid-like definitions of cyclic operads

Guided by the microcosm principle of Baez-Dolan and by the algebraic definitions of operads of Kelly and Fiore, we introduce two "monoid-like" definitions of cyclic operads, one for the original, "exchangable-output" characterisation of Getzler-Kapranov, and the other for the alternative "entries-only" characterisation, both within the category of Joyal's species of structures. Relying on a result of Lamarche on descent for species, we use these "monoid-like" definitions to prove the equivalence between the "exchangable-output" and "entries-only" points of view on cyclic operads.

math.CT↗