## Tagged Questions

2answers
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### What can be said about pairs of matrices P,Q that satisfies $(P^{-1})^T \circ P = (Q^{-1})^T \circ Q$ ?

Let $P,Q$ be $n$ by $n$ invertible matrices. Suppose further that $P$ and $Q$ satisfies the following equation : $$(P^{-1})^T \circ P = (Q^{-1})^T \circ Q$$ where $\circ$ denotes …
0answers
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### 8 queens puzzle

In the 8 queen puzzle, if we use the incremental approach, i.e. put the queen one by one on the board, the number of possible sequences would be 2057. How is that number calculated …
2answers
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### Did Oresme know the zeroth power?

Working on a contribution for a festschrift I touched the introduction of powers. Unfortunately I have no access to the original works of Oresme who was among the first, if not the …
0answers
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### Langlands product

In his 'Märchen' Langlands considers for a local field $F$ a certain abelian category $\Pi(F)$ whose objects are given by isomorphisms classes of irreducible admissible representat …
1answer
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### Surjectivity of the normal exponential map

Given an isometric (in the Riemannian way) immersion $f:N\rightarrow M$ between complete, smooth riemannian manifolds, are there conditions on $M$, $N$, $f$, such that the normal e …
2answers
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### In what rigorous sense are Sperner’s Lemma and the Brouwer Fixed Point Theorem equivalent?

I understand that one can give a proof of each of these propositions assuming the truth of the other. But this seems a bit squishy to me, since there is a trivial sense in which a …
0answers
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### Sperner’s lemma and Tucker’s lemma

In their article "A Borsuk-Ulam Equivalent that Directly Implies Sperner's Lemma" (American Mathematical Monthly, April 2013), Nyman and Su write "[W]e are unaware of a direct proo …

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