esg
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Member for 10 years, 9 months
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Last seen this week
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Determinant of an "almost cyclic" matrix
I'll send you a mail.
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On a problem for determinants associated to Cartan matrices of certain algebras
Ok, thanks (sorry, I should have noticed that). An amazing solution!
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On a problem for determinants associated to Cartan matrices of certain algebras
Small correction to Thm. 1 (I think): $\det(I+Z+\ldots+Z^{\omega(C)-1})$ will be $0$ if $1<\gcd(\omega(C),n)<n$ (so that you can get determinant $0$ also in the connected case).
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On a problem for determinants associated to Cartan matrices of certain algebras
Concerning conjecture 1: is it obvious or easy that the given maxima can be reached? Or is it part of the problem?
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Classification of algebras of finite global dimension via determinants of certain 0-1-matrices
Yes, you are right. Apologies for being sloppy. I'll correct it.
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awarded
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Classification of algebras of finite global dimension via determinants of certain 0-1-matrices
I have just corrected a sign, but nothing essential has changed. The structure of the formula is easy to explain, but I don't see why only the factors +1 and -1 appear. If I don't have a new idea tomorrow I'll post the conjecture.
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Classification of algebras of finite global dimension via determinants of certain 0-1-matrices
You're welcome. Yes, I think it will get more attention with the tags "linear algebra" and "determinants". Feel free to post it - in a sense it is your conjecture (as follow-up of this post).
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Birthday problem extension to unequal probabilities and multiple collisions
simplification and a remark on Schur concavity added
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A question of Ahlswede and Katona: known lower bounds on $\beta(d,n)$?
Take your time. No reason to hurry.
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A question of Ahlswede and Katona: known lower bounds on $\beta(d,n)$?
@Clement C.:I'm surprised that you didn't correct the factor $\tfrac{1}{4}$ in (4) and (5) (you can easily check that in [3] Althöfer/Sillke use definition (1) and give the inequality with factor $\tfrac{1}{2}$). Let me know if I can improve the answer to something useful, in particular if anything is unclear, false, or too succinct.