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An (open?) problem about a sequence of nested principal sub-matrices and their determinants
Problem: Let $A$ be a $n \times n$ integer matrix, $\det(A) = \pm 1$. Under which conditions there exist a nested sequence of principal submatrices of size $n$ such that they all have determinant $\pm …
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How many simplicial complexes on n vertices up to homotopy equivalence?
The sequence A261005 of OEIS should be helpful, since it is an upper bound. However, I don't know any closed formula for the number of simplicial complexes on n unlabeled vertices (without the homotop …