𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Cyclic Model forPG(n, q) and a Construction of Arcs

✍ Scribed by Giorgio Faina; György Kiss; Stefano Marcugini; Fernanda Pambianco

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
64 KB
Volume
23
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

The n-dimensional finite projective space, P G(n, q), admits a cyclic model, in which the set of points of P G(n, q) is identified with the elements of the group Z q n +q n-1 +•••+q+1 . It was proved by Hall (1974, Math. Centre Tracts, 57, 1-26) that in the cyclic model of P G(2, q), the additive inverse of a line is a conic. The following generalization of this result is proved:

In the cyclic model of P G(n, q), the additive inverse of a line is a (q + 1)-arc if n + 1 is a prime and q + 1 > n.

It is also shown that the additive inverse of a line is always a normal rational curve in some subspace P G(m, q), where m + 1|n + 1.

📜 SIMILAR VOLUMES

Types of superregular matrices and the n
Types of superregular matrices and the number of n-arcs and complete n-arcs in PG (r, q)
✍ Gerzson Kéri 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB

## Abstract Based on the classification of superregular matrices, the numbers of non‐equivalent __n__‐arcs and complete __n__‐arcs in PG(__r__, __q__) are determined (i) for 4 ≤ __q__ ≤ 19, 2 ≤ __r__ ≤ q − 2 and arbitrary __n__, (ii) for 23 ≤ __q__ ≤ 32, __r__ = 2 and __n__ ≥ q − 8<$>. The equivale

ChemInform Abstract: The Biomimetic Cons
ChemInform Abstract: The Biomimetic Construction of Fused Cyclic Polyethers.
✍ N. HAYASHI; K. FUJIWARA; A. MURAI 📂 Article 📅 2010 🏛 John Wiley and Sons ⚖ 31 KB 👁 2 views

The Biomimetic Construction of Fused Cyclic Polyethers. -The biomimetic synthesis of naturally occurring fused cyclic ethers by successive ring closure methods is investigated for simple model systems. The one-pot successive ring expansion reactions of bromo trans,trans-diepoxides promoted by AgOTf