All Questions
Tagged with finite-geometry co.combinatorics
13 questions with no upvoted or accepted answers
9
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245
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Almost blocking sets in $\mathbb F_q^2$
$\newcommand{\F}{{\mathbb F}}$
Let $q$ be an odd prime power. A blocking set in the affine plane $\F_q^2$ is a set blocking (meeting) every line.
A union of two non-parallel lines is a blocking set ...
- 23k
8
votes
0
answers
159
views
The Maximum Number of Lines Contained in the Point Set of a Finite Projective Plane
Consider a finite projective plane of order $q$. Define $f(m)$ to be the maximum number of lines completely contained in any point set of size $m$, where $1 \leq m \leq q^2+q+1$. I would like to ...
user48028
7
votes
0
answers
301
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Arrangement of subspaces over finite fields
I'm trying to find out what is already known about the following setup.
Let $V$ be an $n$-dimensional vector space over a finite field $F_q$ (I'm mostly interested in the case where $q$ is prime), and ...
- 1,062
5
votes
0
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235
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A question on hyperplanes in partial linear spaces and hypergraphs
A partial linear space (or a linear hypergraph) is a point line geometry $(P,L,I)$ where for every pair of points there is at most one line incident with both of them. A hyperplane in a partial linear ...
- 1,197
4
votes
0
answers
143
views
Non-Desarguesian finite projective planes with ≤3 (non-collinear) chosen points, and coordinatisation
It is well-known that an arbitrary projective plane can have very different symmetry group to a field plane. In particular, the symmetries are not transitive on the set of fundamental quadrangles. ...
- 35.5k
4
votes
0
answers
250
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Birkhoff – von Neumann for "$k$-stochastic matrices"
Recall that a doubly-stochastic matrix is a square matrix with non-negative elements such the sum of the elements in every row, as well as in every column, is $1$. The set of doubly-stochastic ...
- 23k
4
votes
0
answers
192
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Forcing scalar products to avoid prescribed values
Let $p$ be a prime, and $n\ge 1$ an integer number. Suppose that the (not necessarily distinct) vectors $v_1,\dotsc,v_N \in{\mathbb F}_p^n$ satisfy the following condition:
\begin{gather}
\text{For ...
- 23k
4
votes
0
answers
242
views
Sets of spreads in graphs
Let $G$ be a graph. A $k$-spread is a set of cliques of order $k$ which partition the vertex set (so $k|n$, where $n$ is the number of vertices).
A partial $k$-resolution of $G$ is a set of pairwise ...
- 6,962
3
votes
0
answers
127
views
$\left< 15\right>^7/15$-womcode construction
In the article Womcodes constructed with projective geometries Frans Merkx constructed several good wom-codes (write-once memory codes, see How to reuse a "write-once" memory by Rivest & Shamir ...
- 12.3k
3
votes
0
answers
100
views
Applications of finite Bolyai-Lobachevsky planes
Google scholar gives more than 200 articles comcerning finite Bolyai-Lobachevsky (BL) planes. Usually they devoted to construction of such objects (axioms may be different).
Are their any ...
- 12.3k
2
votes
0
answers
86
views
A system of homogeneous linear equations
This is the "real-life" (but slightly more technical) version of a question I have asked recently.
For a prime $p>10$, let $\mathcal L_X$, $\mathcal L_Y$, and $\mathcal L_Z$ denote the pencils of ...
- 23k
2
votes
0
answers
337
views
Enumerating certain types of permutation polynomials
Given a prime power $q$, I would like to enumerate (preferably up to isomorphism*) all the permutation polynomials $f(x)$ on $K = GF(q^3)$ satisfying the following conditions:
$f(ax) = af(x)$ for all ...
- 1,197
2
votes
0
answers
251
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A problem in Galois Geometry
Given a prime $p$, out of $N$ vectors of length $p^k$ over $\Bbb F_2$ of Hamming weight $w^{k}$ that are chosen, how many vectors can there be with pairwise Hamming distance at least $2w^{k}$ given ...
- 13.9k