Related papers: An Exceptional Combinatorial Sequence and Standard…
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely…
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.
We exhibit an identity of abstract simplicial complexes between the well-studied complex of trees and the reduced minimal nested set complex of the partition lattice. We conclude that the order complex of the partition lattice can be…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
The problem of enumerating meanders -- pairs of simple plane curves with transverse intersections -- was formulated about forty years ago and is still far from solved. Recently, it was discovered that meanders admit a factorization into…
We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…
New regularities found in the pseudoscalar meson octet are reported. They invite to reconsider models where elementary fermions and composite QCD open strings can be grouped in common supermultiplets. It is proven that, with fermions having…
Exceptional points (EPs) are singular points on a parameter space at which some eigenvalues (scattering poles) and their corresponding eigenmodes coalesce. This study shows the existence of second- and third-order EPs in cylindrical elastic…
The present paper studies existence and distributional uniqueness of subclasses of stationary hard-core particle systems arising as thinnings of stationary particle processes. These subclasses are defined by natural maximality criteria. We…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
We define and study root graded groups, that is, groups graded by finite root systems. This notion generalises several existing concepts in the literature, including in particular Jacques Tits' notion of RGD-systems. The most prominent…
It is known that there are infinitely many exceptional sequences of quiver representations for Euclidean quivers. In this paper we study those of type $\tilde{\mathbb{A}}_n$ and classify them into finitely many parametrized families. We…
We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…