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Results tagged with finite-geometry
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user 125498
Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.
4
votes
1
answer
180
views
Is there a unique Baer subplane in a finite Desarguesian projective plane?
An order-$m$ subplane of a finite projective plane of order $n$ is called a Baer subplane if $n=m^2$.
It is known that the projective plane $PG(2,q)$ is a Baer subplane of the Desarguesian projectiv …
- 9,501
11
votes
1
answer
264
views
Does every $C_4$-free bipartite graph lies in some finite projective plane?
A projective plane $Π$ is a 3-tuple $(P,L,I)$ where $P$ and $L$ are sets, and $I$ is a relation between $P$ and $L$, such that:
For every two elements $p_1$, $p_2\in P$, there exists a unique eleme …
- 9,501
9
votes
1
answer
398
views
Are bipartite Moore graphs Hamiltonian?
This is motivated by a computer-generated conjecture that bipartite distance-regular graphs are hamiltonian. I decided to check the case of Moore graphs first.
The cycles and complete bipartite graphs …
- 9,501
16
votes
1
answer
392
views
Geometric interpretation of the exceptional isomorphism $PSp(4,3)=PSU(4,2^2)$
It is well-known that there is an isomorphism between $PSp(4,3)$ (the symplectic group of dimension $4$ over $\mathbb F_3$) and $PSU(4,2^2)$ (the unitary group defined by $4\times4$ unitary matrices …
- 9,501