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8 votes
2 answers
972 views

Incidence geometry and matrices

Supposing I have a $0/1$ or $\pm1$ matrix $A$ of size $m\times n$, is there a minimum $d$ (that works for every $m\times n$ $A$) such that there exists $m$ lines $r_1,\dots,r_m$, $n$ lines $s_1,\dots,...
Turbo's user avatar
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2 votes
1 answer
302 views

For which finite projective planes can the incidence structure be written as a circulant matrix?

It is well known that the projective plane of order $2$ can be represented by the circulant matrix $M_2:=circ(x,x,1,x,1,1,1)= \begin{pmatrix} x&x&1&x&1&1&1\\ 1&x&x&...
Wolfgang's user avatar
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2 votes
0 answers
72 views

Lexicographically largest incidence matrix

I have simple algorithmic question, but I can't find any source where this algorithm is explained in details. Let's assume that we have incidence (with 0 and 1 values) matrix of size $m\times n$. Let ...
Ihromant's user avatar
  • 511
2 votes
0 answers
267 views

On the determinant of incidence matrices (of graphs and other geometries)

Let $\Gamma = (P,L,I)$ be a point-line geometry (here, $P$ is the point set, $L$ the line set, and $I$ is the symmetric incidence relation). (As an example, $\Gamma$ could be a graph.) I suppose $\...
THC's user avatar
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