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We find by applying MacMahon's partition analysis that all magic labellings of the cube are of eight types, each generated by six basis elements. A combinatorial proof of this fact is given. The number of magic labellings of the cube is…

Much of dynamical algebraic combinatorics focuses on global dynamical systems defined via maps that are compositions of local toggle operators. The second author and Roby studied such maps that result from toggling independent sets of a…

Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…

Passing from arithmetic schemes to algebraic schemes, in a similar manner we will have the computation of the \'etale fundamental group of an algebraic scheme and then will define and discuss the qc fundamental group of an algebraic scheme…

We study the Hulek--Verrill families of Calabi--Yau threefolds. They are birationally equivalent to fibred products of elliptic surfaces, so we expect to be able to compute periods on these threefolds by integrating products of elliptic…

Tilings and tiling systems are an abstract concept that arise both as a computational model and as a dynamical system. In this paper, we characterize the sets of periods that a tiling system can produce. We prove that up to a slight…

We study central extensions of nilpotent loops by elementary abelian $p$-groups using normalized cocycles. By introducing an affine automorphism group acting on the full cocycle space, we obtain a direct correspondence between affine orbits…

The conjugation action of the complex orthogonal group on the polynomial functions on $n \times n$ matrices gives rise to a graded algebra of invariant polynomials. A spanning set of this algebra is in bijective correspondence to a set of…

The inverse Kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics. In this paper, we consider three…

We have analysed publicly available MACHO observations of 6833 variable stars in the Large Magellanic Cloud, classified as eclipsing binaries. After finding that a significant fraction of the sample was misclassified, we redetermined…

The presence of a massive close-in planet with an orbital period of a few days or less around a low-mass star can possibly results in a strong variation of the properties of the central star. Indeed, star-planet tidal interactions generate…

We present a detailed study of the classical Cepheid in the double-lined, highly eccentric eclipsing binary system OGLE-LMC562.05.9009. The Cepheid is a fundamental mode pulsator with a period of 2.988 days. The orbital period of the system…

We consider Riordan arrays $\bigl(1/(1-t^{d+1}), ~ tp(t)\bigr)$. These are infinite lower triangular matrices determined by the formal power series $1/(1-t^{d+1})$ and a polynomial $p(t)$ of degree $d$. Columns of such matrix are eventually…

Relativistic secular perturbation theory has ignited significant interest in uncovering intricate cross-term effects, especially the interplay between 1PN and quadrupole terms. While most existing studies rely on the Lagrangian planetary…

We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order $n$. We compute the Plancherel measure of the representation using Eisenstein series and a comparison…

We explain that the set of new integrable systems generalizing the Calogero family and implied by the study of WLZZ models, which was described in arXiv:2303.05273, is only the tip of the iceberg. We provide its wide generalization and…

The traditional time series methodology requires at least a preliminary transformation of the data to get stationarity. On the other hand, Robust Bayesian Dynamic Models (RBDMs) do not assume a regular pattern or stability of the underlying…

The solar cycle is generated by a magnetohydrodynamic dynamo mechanism which involves the induction and recycling of the toroidal and poloidal components of the Sun's magnetic field. Recent observations indicate that the Babcock-Leighton…

We study topological properties of circularly ordered dynamical systems and prove that every such system is representable on a Rosenthal Banach space, hence, is also tame. We derive some consequences for topological groups. We show that…

VW~LMi is the tightest known quadruple system with 2+2 hierarchy. It consists of a W UMa-type eclipsing binary (P12 = 0.47755 days) and another detached non-eclipsing binary (P34 = 7.93 days) orbiting around a common center of mass is about…