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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
An algorithm to find non-trivial linear dependencies
There are results pertaining to the finite field case. According to this paper, for a finite field $F_q$ and a set of $r$ points $x_1,\dotsc,x_r\in F_q^n$ deciding whether there exists a subset of $k$ …
3
votes
0
answers
82
views
Matroid rank decay
Consider a uniform vector matroid $M(0)=U_{m,n}$ of rank $m$ with $n$ points, $n>m>2$ (you can think of it as a set of $n$ points in general position in vector space $F^m$ for some large field $F$). W …