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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.
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How many minors I need to check to conclude all minors will vanish ?
For any set of $(j_i)_{i=1}^m$, with $1\le j_1 < \cdots < j_m \le n$, let $A$ be the matrix with elements $A_{ij} = \delta_{ij_i}$. Every minor except the one defined by the columns $j_i$ vanishes, so …