Now showing items 1-10 of 22
The circle space of a spherical circle plane
(BELGIAN MATHEMATICAL SOC TRIOMPHE, 2014)
We show that the circle space of a spherical circle plane is a punctured projective 3-space. The main ingredient is a partial solution of the problem of Apollonius on common touching circles.
On kleinewillingh¨ofer types of finite laguerre planes with respect to homotheties
© 2016, University of Queensland. All rights reserved. Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms and obtained a multitude of types. In this paper we investigate the Kleinewillinghöfer ...
Maps between curves and arithmetic obstructions
Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family ...
Asymptotic enumeration of symmetric integer matrices with uniform row sums
(CAMBRIDGE UNIV PRESS, 2013)
We investigate the number of symmetric matrices of nonnegative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero-diagonal symmetric contingency tables with uniform margins, or ...
Maximal differential uniformity polynomials
We provide an explicit infinite family of integers m such that all the polynomials of F2n [x] of degree m have maximal differential uniformity for n large enough. We also prove a conjecture of the third author in these cases.
New characterisations of tree-based networks and proximity measures
Phylogenetic networks are a type of directed acyclic graph that represent how a set X of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of ...
Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos
We describe the structure of Tate-Shafarevich groups of a constant elliptic curves over function fields by exploiting the volcano structure of isogeny graphs of elliptic curves over finite fields.
Improved rank bounds from 2-descent on hyperelliptic Jacobians
© 2018 World Scientific Publishing Company. We describe a qualitative improvement to the algorithms for performing 2-descents to obtain information regarding the Mordell-Weil rank of a hyperelliptic Jacobian. The improvement ...
On automorphism groups of toroidal circle planes
© 2018, Springer International Publishing AG, part of Springer Nature. Schenkel proved that the automorphism group of a flat Minkowski plane is a Lie group of dimension at most 6 and described planes whose automorphism ...
The Drinker Paradox and its Dual
The Drinker Paradox is as follows. In every nonempty tavern, there is a person such that if that person is drinking, then everyone in the tavern is drinking. Formally, \[ \exists x \big(\varphi \rightarrow \forall ...