On KM-Arcs in Small Desarguesian Planes

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On KM-Arcs in Small Desarguesian Planes

In this paper we study the existence problem for KM-arcs in small Desarguesian planes. We establish a full classification of KMq,t-arcs for q 6 32, up to projective equivalence. We also construct a KM64,4-arc; as t = 4 was the only value for which the existence of a KM64,t-arc was unknown, this fully settles the existence problem for q 6 64.

متن کامل

Maximal Arcs in Desarguesian Planes

A ( k , n ) a r c in a projective plane is a set of k points, at most n on every line. If the order of the plane is q, then k < 1 + (q + 1) (n 1) = qn q + n with equality if and only if every line intersects the arc in 0 or n points. Arcs realizing the upper bound are called maximal arcs. Equality in the bound implies tha t n lq or n = q + l . If 1 < n < q, then the maximal arc is called non-tr...

متن کامل

On Mathon’s construction of maximal arcs in Desarguesian planes

We study the problem of determining the largest d of a non-Denniston maximal arc of degree 2 generated by a fp; 1g-map in PGð2; 2Þ via a recent construction of Mathon [9]. On one hand, we show that there are fp; 1g-maps that generate non-Denniston maximal arcs of degree 2ðmþ1Þ=2, where md 5 is odd. Together with Mathon’s result [9] in the m even case, this shows that there are always fp; 1g-map...

متن کامل

On Mathon's construction of maximal arcs in Desarguesian planes II

In a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when m ≥ 5 and m 6= 9, th...

متن کامل

Arcs in Desarguesian nets

A trivial upper bound on the size k of an arc in an r-net is k ≤ r + 1. It has been known for about 20 years that if the r-net is Desarguesian and has odd order, then the case k = r + 1 cannot occur, and k ≥ r−1 implies that the arc is contained in a conic. In this paper, we show that actually the same must hold provided that the difference r − k does not exceed p k/18. Moreover, it is proved t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2017

ISSN: 1077-8926

DOI: 10.37236/6057