Related papers: A Note on Boolean Lattices and Farey Sequences III

We describe a natural geometric relationship between matroids and underlying flag matroids by relating the geometry of the greedy algorithm to monotone path polytopes. This perspective allows us to generalize the construction of underlying…

We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…

We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves…

In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.

We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of…

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.

We show that, up to minor-equivalence, the Farey graph is the unique minor-minimal graph that is infinitely edge-connected but such that every two vertices can be finitely separated.

We construct a monadic second-order sentence that characterizes the ternary relations that are the betweenness relations of finite or infinite partial orders. We prove that no first-order sentence can do that. We characterize the partial…

We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between…

In bilayer CrI3, experimental and theoretical studies suggest that the magnetic order is closely related to the layer staking configuration. In this work, we study the effect of dynamical lattice distortions, induced by non-linear phonon…

We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present…

Haros graphs is a graph-theoretical representation of real numbers in the unit interval. The degree distribution of the Haros graphs provides information regarding the topological structure and the associated real number. This article…

We prove an analogue of the Oppenheim conjecture for a system comprising an inhomogeneous quadratic form and a linear form in $3$ variables using dynamics on the space of affine lattices.

The intersection distribution of a polynomial $f$ over finite field $\mathbb{F}_q$ was recently proposed in Li and Pott (arXiv:2003.06678v1), which concerns the collective behaviour of a collection of polynomials $\{f(x)+cx \mid c \in…

The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…

Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…

When a series of measurements is performed with increasingly coarse (or increasingly fine) precision, consecutive observations seem to be erratically distributed at first, and then organize themselves into cycles and patterns. The patterns,…

Consider the number of permutations in the symmetric group on n letters that contain c copies of a given pattern. As c varies (with n held fixed) these numbers form a sequence whose properties we study for the monotone patterns and the…