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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
0 answers
73 views

Degeneracy and the "Linear Degeneracy Testing" problem

The Affine Degeneracy problem is about deciding whether $n$ given points in $\mathbb{R}^d$ (or $\mathbb{Q}^d$) are "in general position". i.e. there is no $d+1$ tuple of points which lies in a $d-1$ d …
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4 votes
1 answer
209 views

Finding a binary variable assignment to make a matrix with variables singular (over F_p)

Consider a square matrix defined over a finite field $M\in\mathbb{F}_p^{n\times n}$ having the following form $$M=\begin{bmatrix}a_{11}+b_{11}x_1&a_{12}+b_{12}x_1&\dots&a_{1n}+b_{1n}x_1\\a_{21}+b_{21} …
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  • 153