Related papers: A new partial geometry pg(5,5,2)
We give a new construction of the Mathon perp-system of the five dimensional projective space over the field with three elements, starting from four lines.
For an oriented surface of genus g with b boundary components, we construct a rational map from a subset of C^{6g-6+3b} onto an open algebraic subset of the PSL(2,C)-character variety as an analogue of the Fenchel-Nielsen coordinates. After…
We present a new construction of non-classical unitals from a classical unital $U$ in $PG(2,q^2)$. The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model $\Pi$ of $PG(2,q^2)$ with the following three…
Parametric geometry of numbers is a new theory, recently created by Schmidt and Summerer, which unifies and simplifies many aspects of classical Diophantine approximations, providing a handle on problems which previously seemed out of…
A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering. The circular separation dimension of a graph $G$, denoted by $\pi^\circ(G)$, is the…
In this paper we find the number of different signatures of $P(3,1), P(5,1)$ and $P(7,1)$ upto switching isomorphism, where $P(n, k)$ denotes the generalised Petersen graph, $2k < n$. We also count the number of non-isomorphic signatures on…
We provide sharp bounds for the isoperimetric constants of infinite plane graphs (tessellations) with bounded vertex and face degrees. For example, if $G$ is a plane graph satisfying the inequalities $p_1 \leq \mbox{deg}\ v \leq p_2$ for $v…
We use the method of synthetic differential geometry to revisit the geometric reasoning employed by Lie, Klein and others in their study of partial differential equations.
For an incidence geometry $\mathcal{G} = (\mathcal{P}, \mathcal{L}, \text{I})$ with a linear representation $\mathcal{T}_n^*(\mathcal{K})$, we apply WQH switching to construct a non-geometric graph $\Gamma'$ cospectral with the line graph…
A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique…
We give a large family of almost perfect nonlinear (APN) permutations of finite vector spaces of every odd dimension divisible by three. We also give APN functions that are not bijective on even dimensions and related highly nonlinear…
We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex…
This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give upper and lower bounds for the minimal number of triangles…
The two parameter quantum group G_r,s is generated by five elements, four of which form a Hopf subalgebra isomorphic to GL_q(2), while the fifth generator relates G_r,s to GL_p,q(2). We construct explicitly the dual algebra of G_r,s and…
A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
We say that a graph $G$ is $(2,m)$-linked if, for any distinct vertices $a_1,\ldots, a_m, b_1,b_2$ in $G$, there exist vertex disjoint connected subgraphs $A,B$ of $G$ such that $\{a_1, \ldots, a_m\}$ is contained in $A$ and $\{b_1,b_2\}$…
The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or…
The paper presents the geometry of the non-linear least squares adjustment using the Palzan lemma.
We consider the orbits of the group $G=PGL_2(q)$ on the points, lines and planes of the projective space $PG(3,q)$ over a finite field $\mathbb F_q$ of characteristic different from $2$ and $3$. The points of $PG(3,q)$ can be identified…