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Results tagged with incidence-geometry
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user 12858
Abstract incidence geometries like projective spaces, polar spaces, generalized polygons, as well as incidence problems in the real or complex Euclidean spaces (eg. Szemerédi–Trotter theorem).
10
votes
Accepted
Which finite projective planes can have a symmetric incidence matrix?
The key word here is "polarity". A polarity of a projective plane with point set $P$ and line set $L$ is a map $\pi$ from $P \cup L$ to itself mapping points to lines and lines to points, such that $\ …
- 6,614
9
votes
Accepted
What is the automorphism group of this geometry?
Your geometry has the property that each of its rank 2 restrictions is a Fano plane. In particular, the type-preserving automorphism group (let's call it $G$) is a subgroup of the automorphism group o …
- 6,614
6
votes
Synthetic projective lines
Following up on Matthias Wendt's comment, the language of Moufang sets is indeed a suitable axiomatic approach to (generalizations of) projective lines.
Formally speaking, a Moufang set is a set $X$ …
- 6,614
4
votes
Ree groups and Moufang octagons
Only having $k$ as subfield of $\ell$ is not sufficient (for both questions). The Ree groups (and the generalized octagons) are determined by a pair $(k, \theta)$, where $k$ is a field of characterist …
- 6,614