Poncelet's Theorem in the four nonisomorphic finite projective planes of order 9

A Poncelet Criterion for special pairs of conics in $PG(2,p)$

We study Poncelet's Theorem in finite projective coordinate planes over the field $GF(p)$ and concentrate on a particular pencil of conics. For pairs of such conics we investigate whether we can find polygons with $n$ sides, which are inscribed in one conic and circumscribed about the other, so-called Poncelet Polygons. By using suitable elements of the dihedral group for these pairs, we prove that the length $n$ of such Poncelet Polygons is independent of the starting point. In this sense Poncelet's Porism is valid. By using Euler's divisor sum formula for the totient function, we can make a …

彭赛列多边形的显式构造

Explicit Constructions for Poncelet Polygons

本文从射影角度研究彭赛列n边形，给出特定n下的显式构造与括号多项式代数刻画，利用其与(N₄)-构型的关联，构造出此前被认为刚性的可动平凡天体4-构型。

Maximal arcs, codes, and new links between projective planes

In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes. Upper and lower bounds on the 2-rank of the incidence matrices are derived. A lower bound on the minimum distance of the dual codes is proved, and it is shown that the bound is achieved if and only if the related maximal arc contains a hyperoval of the plane. The binary linear codes of length 52 spanned by the incidence matrices of 2-$(52,4,1)$ designs associated with previously known and some newly found maximal…

Experimental Results of the Search for Unitals in Projective Planes of Order 25

In this paper we present the results from a program developed by the author that finds the unitals of the known 193 projective planes of order 25.. There are several planes for which we have not found any unital. One or more than one unitals have been found for most of the planes. The found unitals for a given plane are nonisomorphic each other. There are a few unitals isomorphic to a unital of another plane. A t - (v; k; λ) design D is a set X of points together with a family B of k-subsets of X called blocks with the property that every t points are contained in exactly λ blocks. The design …