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16
votes
1
answer
867
views
Compact contractible topological manifold with boundary=sphere is a ball
(this question is joint with Steven Karp and Thomas Lam) We need to use the following fact in our paper:
Theorem 1. Let $M^n$ be a compact contractible topological manifold with boundary, such tha …
5
votes
1
answer
212
views
Reconstructing an oriented matroid from its deletion and contraction
Suppose that $\mathcal{M}_1$ and $\mathcal M_2$ are two oriented matroids on the same ground set $E$. Under what conditions on $\mathcal{M}_1$ and $\mathcal{M}_2$ is there an oriented matroid $\mathca …
3
votes
Accepted
Reconstructing an oriented matroid from its deletion and contraction
Found the answer in a paper by Ziegler & Richter-Gebert, see Theorem 4.1. Basically, they show that if two oriented matroids $\mathcal{M}_1$, $\mathcal{M}_2$ of ranks $r$ and $r-1$ respectively satis …
4
votes
Tableaux with limited rows and complementary skew shapes
Here is another solution, based on the paper "Robinson-schensted algorithms for skew tableaux" by Sagan and Stanley (Darij Grinberg was the one who suggested that this algorithm might work, I'm just f …