Related papers: Linear extensions and continued fractions
We study the generalized continued fraction expansions of complex numbers in term of elements from Euclidean subrings, especially Gaussian or Eisenstein integers, in a general framework as pursued in [3] and [1]. We introduce a common…
The linear extension diameter of a finite poset P is the maximum distance between a pair of linear extensions of P, where the distance between two linear extensions is the number of pairs of elements of P appearing in different orders in…
We study explicit continued fraction expansions for certain series. Some of these expansions have symmetry that generalizes some remarkable examples discovered independently by Kmosek and Shallit. Furthermore, we prove the following…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
In this paper we show how to apply various techniques and theorems (including Pincherle's theorem, an extension of Euler's formula equating infinite series and continued fractions, an extension of the corresponding transformation that…
We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field $\mathbb Q(\sqrt D)$ and obtain lower and upper bounds for it in terms of certain sums of…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce the connective implication to be everywhere defined and satisfying (left) adjointness with the connective…
In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of ${\mathbb Q}_p$ over ${\mathbb Q}$ and gives a finite expansion for every rational number. We also give,…
Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $\mathfrak P$-adic continued fractions satisfying the finiteness property on $K$ for…
In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
Given a finite poset P, we consider pairs of linear extensions of P with maximal distance, where the distance between two linear extensions L_1, L_2 is the number of pairs of elements of P appearing in different orders in L_1 and L_2. A…
We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…