Related papers: Linear degree growth in lattice equations
We study linear evolution equations in separable Hilbert spaces defined by a bounded linear operator. We answer the question which of these equations can be written as a gradient flow, namely those for which the operator is real…
It was studied the growth of Temperley-Lieb type algebras with orthogonal and commutative relations associated with 2-colored edges graphs. Depending on the structure of the graphs they can be finite-dimensional or to have linear or…
It is proved that the rectilinear crossing number of every graph with bounded tree-width and bounded degree is linear in the number of vertices. **** This paper has been withdrawn by the author. **** The results have been superseeded by the…
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We investigate the compatibility of Lorentzian amalgamation with various properties of Lorentzian pre-length spaces. In particular, we give conditions under which gluing of Lorentzian length spaces yields again a Lorentzian length space and…
We study the equational theory of the Weihrauch lattice with composition and iterations, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the composition operator $\star$ and…
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We show that one can define through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole-Hopf transformation. If the equation is linearizable the symmetry provides the…
The degree sequence of the algebraic numbers in an algebraic linear recurrence sequence is shown to be virtually periodic. This is proved using the Skolem-Mahler-Lech theorem. It has applications to the degree sequence and the minimal…
We formulate the notion of continuous evolution algebra in terms of differentiable matrix-valued functions, to then study those such algebras arising as solutions of ODE problems. Given their dependence on natural bases, matrix Lie groups…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…
We show that any graph polynomial from a wide class of graph polynomials yields a recurrence relation on an infinite class of families of graphs. The recurrence relations we obtain have coefficients which themselves satisfy linear…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
We study the central extensions of Lie algebras graded by an irreducible locally finite root system.
Two lattice points are visible to one another if there exist no other lattice points on the line segment connecting them. In this paper we study convex lattice polygons that contain a lattice point such that all other lattice points in the…