On Near Hexagons and Spreads of Generalized Quadrangles

نویسنده

  • BART DE BRUYN
چکیده

The glueing-construction described in this paper makes use of two generalized quadrangles with a spread in each of them and yields a partial linear space with special properties. We study the conditions under which glueing will give a near hexagon. These near hexagons satisfy the nice property that every two points at distance 2 are contained in a quad. We characterize the class of the “glued near hexagons” and give examples, some of which are new near hexagons.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Coordinatization structures for generalized quadrangles and glued near hexagons

A generalized admissible triple is a triple T = (L, X,∆), where X is a set of size s + 1 ≥ 2, L is a Steiner system S(2, s + 1, st + 1), t ≥ 1, with point-set P and ∆ is a very nice map from P × P to the group Sym(X) of all permutations of the set X. Generalized admissible triples can be used to coordinatize generalized quadrangles with a regular spread and glued near hexagons. The idea of coor...

متن کامل

Spreads and ovoids of finite generalized quadrangles

We survey recent results on spreads and ovoids of finite generalized quadrangles. Included in the survey are results on ovoids of PG(3, q); translation ovoids of Q(4, q); characterisations of generalized quadrangles using subquadrangles and ovoids of subquadrangles; and spreads of T2(Ω).

متن کامل

Solution to an open problem on extremal generalized hexagons

A finite generalized 2d-gon of order (s, t) with d ∈ {2, 3, 4} and s 6= 1 is called extremal if t attains its maximal possible value sed , where e2 = e4 = 2 and e3 = 3. The problem of finding combinatorial conditions that are both necessary and sufficient for a finite generalized 2d-gon of order (s, t) to be extremal has so far only be solved for quadrangles and octagons. In this paper, we obta...

متن کامل

Partial Ovoids and Spreads in Generalized Quadrangles, and Related Combinatorial Structures

In this paper we overview what is known about partial ovoids and spreads of finite (classical) generalized quadrangles. In the first, respectively the second, part of the paper we will be mostly concerned with small, respectively large, maximal partial ovoids and spreads. Also connections with other interesting objects in finite geometry will be explained. Among the new results are new bounds o...

متن کامل

On the smallest maximal partial ovoids and spreads of the generalized quadrangles W(q) and Q(4, q)

We present results on the size of the smallest maximal partial ovoids and on the size of the smallest maximal partial spreads of the generalized quadrangles W (q) and Q(4, q).

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000