6 papers
Presheaf structures governed by oriented matroids and pseudohyperplane arrangements
Basile Coron, Denis Lyskov
We study higher complements of pseudohyperplane arrangements and the specialization maps between them, induced by degenerations. We develop a presheaf formalism on oriented matroid…
Graphical configuration spaces, Contractads and Formality
Anton Khoroshkin, Denis Lyskov
Given a finite simple connected graph , the graphical configuration space is the space of collections of points in indexed by the vertices of , where…
Hilbert series for contractads and modular compactifications
Anton Khoroshkin, Denis Lyskov
Contractads are operadic-type algebraic structures well-suited for describing configuration spaces indexed by a simple connected graph . Specifically, these configuration spaces…
Operadic structure on Hamiltonian paths and cycles
Denis Lyskov
We study Hamiltonian paths and cycles in undirected graphs from an operadic viewpoint. We show that the graphical collection encoding directed Hamiltonian paths in c…
A generalization of operads based on subgraph contractions
Denis Lyskov
We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by…
Reconnectads
Vladimir Dotsenko, Adam Keilthy, Denis Lyskov
We introduce a new operad-like structure that we call a reconnectad; the ``input'' of an element of a reconnectad is a finite simple graph, rather than a finite set, and ``composit…