On the number of regions determined bynlines in the projective plane
β Scribed by George Purdy
- Publisher
- Springer
- Year
- 1980
- Tongue
- English
- Weight
- 114 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
An explicit formula for the number of finite cyclic projective planes or planar . Ε½ . 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.
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.
## Abstract In this paper, we show that the projective plane crossing number of the graphs __C__~3~ Γ __C__~__n__~ is __n__ β 1 for __n__ β€ 5 and 2 for __n__ = 4. As far as we can tell from the literature, this is the first infinite family of graphs whose crossing number is known on a single surfac