Related papers: On the geometry behind a recurrent relation
We define and investigate a new three-parameter family of graphs that further generalizes the Fibonacci and metallic cubes. Namely, the number of vertices in this family of graphs satisfies Horadam recurrence, a linear recurrence of second…
For a Markov chain both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical…
In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…
Given a 3-dimensional (para-)CR structure, its family of chains define a 3-dimensional path geometry. We provide necessary and sufficient conditions that determine whether a path geometry in dimension three arises from chains of a CR or…
We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general three-term bilinear recurrence relation of fourth order is given in terms of the Weierstrass sigma function for an associated…
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
A successive vertex ordering of a graph is a linear ordering of its vertices in which every vertex except the first has at least one neighbour appearing earlier. Such orderings arise naturally in incremental growth and…
Ramsey algebras is an attempt to investigate Ramsey spaces generated by algebras in a purely combinatorial fashion. Previous studies have focused on the basic properties of Ramsey algebras and the study of a few specific examples. In this…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
We review our efforts in investigating gauge theories with fermions in the adjoint representation of the gauge group by means of numerical simulations. These theories have applications in possible extensions of the Standard Model of…
We analyze properties of the 2-adic valuations of an integer sequence that originates from an explicit evaluation of a quartic integral. We also give a combinatorial interpretation of the valuations of this sequence. Connections with the…
To the Farey tessellation of the upper half-plane we associate an AF algebra encoding the cutting sequences that define vertical geodesics. The Effros-Shen AF algebras arise as quotients of our algebra. Using the path algebra model for AF…
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…
This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
We study to which extent the family of pairs of subspaces of a vector space related to each other via intersection properties determines the vector space. In another language, we study to which extent the family of vertices of the building…
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…