All Questions
3 questions
2
votes
2
answers
258
views
Equal-valued determinants in search of a proof: Part III
Encouraged by David's proof for my earlier MO question, let's consider a similar problem.
I can prove the below equality by computing each of the two sides, directly. That means, there is an ...
- 43.2k
11
votes
1
answer
579
views
Catalan determinants in search of a proof: Part II
This problem involves the Catalan numbers $C_n=\frac1{n+1}\binom{2n}n$.
I can prove the below equality by computing each of the two sides, directly. That means, there is an algebraic proof.
...
- 43.2k
6
votes
1
answer
535
views
A surprising identity: $\det[\cos\pi\frac{jk}n]_{1\le j,k\le n}=(-1)^{\lfloor\frac{n+1}2\rfloor}(n/2)^{(n-1)/2}$
On the basis of my computation, here I pose my following conjecture involving the cosine function.
Conjecture. For any positive integer $n$, we have the identity
$$\frac1{2n}\det\left[\cos\pi\frac{jk}...
- 15.6k