Related papers: Subpolygons in Conway-Coxeter frieze patterns
In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the…
We produce two-dimensional contiguous relations for generalized hypergeometric functions by starting with linearization coefficients for some continuous generalized hypergeometric orthogonal polynomials in the Askey-scheme.
We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.
Evaluating or finding the roots of a polynomial $f(z) = f_0 + \cdots + f_d z^d$ with floating-point number coefficients is a ubiquitous problem. By using a piecewise approximation of $f$ obtained with a careful use of the Newton polygon of…
We consider formal power series in several variables with coefficients in arbitrary field such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of the power series $f$ to such an edge is a product of…
We study properties of (bi-infinite) arrays having all adjacent $k\times k$ adjacent minors equal to one. If we further add the condition that all adjacent $(k-1)\times (k-1)$ minors be nonzero, then these arrays are necessarily of rank…
The q-binomial coefficients are the polynomial cousins of the traditional binomial coefficients, and a number of identities for binomial coefficients can be translated into this polynomial setting. For instance, the familiar vanishing of…
We consider polynomials expressing the cohomology classes of subvarieties of products of projective spaces, and limits of positive real multiples of such polynomials. We study the relation between these covolume polynomials and Lorentzian…
Tropical Newton-Puiseux polynomials defined as piece-wise linear functions with rational coefficients at the variables, play a role of tropical algebraic functions. We provide explicit formulas for tropical Newton-Puiseux polynomials being…
We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.
Goulden-Rattan polynomials give the exact value of the subdominant part of the normalized characters of the symmetric groups in terms of certain quantities ($C_i$) which describe the macroscopic shape of the Young diagram. The…
We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This family of polytopes contains polyhedral models for the Coxeter-theoretic analogs of…
It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating…
The proper Class $\bf{No}$ of all Conway's numbers $\cite{l3}$ is considered as a region of investigation. It turns out to be a total ordered Field (i.e., a field whose domain is a proper Class) and this totally, or linear ordered Class,…
In this paper, we present a new method for computing the f-vector of a marked order polytope. Namely, given an arbitrary (polyhedral) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field…
The entries of frieze patterns may be interpreted as coordinates of roots of a finite Weyl groupoid of rank two. We prove the existence of maximal elements in their root posets and classify those frieze patterns which can be used to build…
A frieze in the modern sense is a map from the set of objects of a triangulated category $\mathsf{C}$ to some ring. A frieze $X$ is characterised by the property that if $\tau x\rightarrow y\rightarrow x$ is an Auslander-Reiten triangle in…
In this paper we study the structure of polynomials of degree three and four that have high bias or high Gowers norm, over arbitrary prime fields. In particular we obtain the following results. 1. We give a canonical representation for…
A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…
We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful…