✦ LIBER ✦

On the Number of Cyclic Projective Planes

✍ Scribed by John Konvalina

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 141 KB
Volume: 20
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1997.0569

No coin nor oath required. For personal study only.

✦ Synopsis

An explicit formula for the number of finite cyclic projective planes or planar . Ž . difference sets is derived by applying Ramanujan sums Von Sterneck numbers and Mobius inversion over the set partition lattice to counting one-to-one solution vectors of multivariable linear congruences.

📜 SIMILAR VOLUMES

Upper chromatic number of finite project

Upper chromatic number of finite projective planes

✍ Gábor Bacsó; Zsolt Tuza 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 135 KB

## Abstract For a finite projective plane $\Pi$, let $\bar {\chi} (\Pi)$ denote the maximum number of classes in a partition of the point set, such that each line has at least two points in the same partition class. We prove that the best possible general estimate in terms of the order of projectiv

The Number of Loopless 4-Regular Maps on

The Number of Loopless 4-Regular Maps on the Projective Plane

✍ Han Ren; Yanpei Liu 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 175 KB

In this paper rooted loopless (near) 4-regular maps on surfaces such as the sphere and the projective plane are counted and exact formulae with up to three or four parameters for such maps are given. Several classical results on regular maps and one-faced maps are deduced.

On Bounding the Number of Generators for

On Bounding the Number of Generators for Fat Point Ideals on the Projective Plane

✍ Stephanie Fitchett 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 145 KB

Let X be the surface obtained by blowing up general points p 1 p n of the projective plane over an algebraically closed ground field k, and let L be the pullback to X of a line on the plane. If C is a rational curve on X with C • L = d, then for every t there is a natural map C C t ⊗ X X L → C C t +

The Center of Some Quantum Projective Pl

The Center of Some Quantum Projective Planes

✍ Izuru Mori 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 209 KB

The homogeneous coordinate ring of a quantum projective plane is a 3-dimensional Artin᎐Schelter regular algebra with the same Hilbert series as the polynomial ring in three variables; such an algebra A is a graded noncommutative analogue of the polynomial ring in three variables. When A is a finite

On the Number of Planes in Neumaier's A8

On the Number of Planes in Neumaier's A8-Geometry

✍ Philippe Cara 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 55 KB

In one of his papers [2], A. Neumaier constructed a rank 4 incidence geometry on which the alternating group of degree 8 acts flag-transitively. This geometry is quite important since its point residue is the famous A 7 -geometry which is known to be the only flag-transitive locally classical C 3 -g

Hyperovals in the known projective plane

Hyperovals in the known projective planes of order 16

✍ Tim Penttila; Gordon F. Royle; Michael K. Simpson 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 382 KB

We construct by computer all of the hyperovals in the 22 known projective planes of order 16. Our most interesting result is that four of the planes contain no hyperovals, thus providing counterexamples to the old conjecture that every finite projective plane contains an oval.