Related papers: Activity from matroids to rooted trees and beyond
We generalize Exel's notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably well-behaved systems of generators and relations, we employ classical rewriting theory in order to describe…
For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is…
The mechanisms responsible for contention of activity in systems represented by networks are crucial in various phenomena, as in diseases such as epilepsy that affects the neuronal networks, and for information dissemination in social…
The paper is concerned with the space of the marked Schreier graphs of the Grigorchuk group and the action of the group on this space. In particular, we describe an invariant set of the Schreier graphs corresponding to the action on the…
We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acts absolutely non-freely on the boundary of the…
In this note we introduce a family of polynomials on a matroid derived from chain Tutte polynomials which generalize the classic and ubiquitous characteristic polynomial. We show that the coefficients of these polynomials alternate and…
Recent developments in network neuroscience have highlighted the importance of developing techniques for analyzing and modeling brain networks. A particularly powerful approach for studying complex neural systems is to formulate generative…
We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality…
Originally in 1954 the Tutte polynomial was a bivariate polynomial associated to a graph in order to enumerate the colorings of this graph and of its dual graph at the same time. However the Tutte polynomial reveals more of the internal…
Scattering amplitudes for colored theories have recently been formulated in a new way, in terms of curves on surfaces. In this note we describe a canonical set of functions we call surface functions, associated to all orders in the…
We extend the hyperplane arrangement framework for neural network expressivity from the braid to discriminantal arrangements. Compatible piecewise linear functions are characterized by circuit relations and admit a matroidal description via…
An algebraic formalism, developped with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized…
Let G(d,n) denote the Grassmannian of d-planes in C^n and let T be the torus (C^*)^n/diag(C^*) which acts on G(d,n). Let x be a point of G(d,n) and let \bar{Tx} be the closure of the T-orbit through x. Then the class of the structure sheaf…
We use motivic colimits to construct power operations on the homotopy groups of normed motivic spectra admitting a (normed) map from HF_2. We establish enough of their standard properties to prove that the motivic dual Steenrod algebra is…
We construct an infinite tower of covering spaces over the configuration space of $n-1$ distinct non-zero points in the complex plane. This results in an action of the braid group $\mathbb{B}_n$ on the set of $n$-adic integers…
We study the expressivity of rational neural networks (RationalNets) through the lens of algebraic geometry. We consider rational functions that arise from a given RationalNet to be tuples of fractions of homogeneous polynomials of fixed…
An operation on species corresponding to the inner plethysm of their associated cycle index series is constructed. This operation, the inner plethysm of species, is generalized to n-sorted species. Polynomial maps on species are studied and…
We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous…
Motivated by the Gray code interpretation of Hamiltonian cycles in Cayley graphs, we investigate the existence of Hamiltonian cycles in tope graphs of hyperplane arrangements, with a focus on simplicial, reflection, and supersolvable…
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…