Erik
Reputation
Top tag
Next privilege 250 Rep.
 Sep9 comment Strange factorial identity From OEIS it seems the number of elements in G_{n,k} should be the number of n-permutations with exactly k consecutive cycles (oeis.org/A184184). I cannot see whether your bijection proves this stronger claim. Sep3 comment Game involving points on $[0,1]$ @ChristianBlatter: Nice graph! It'd be interesting to see it for larger n. If one wants one of the final points to be 0, then one cannot do better than (1+a)/2^(n-2). Otherwise, the final points are 1/2^k and a/2^l for some (k,l) such that k+l <= n-2. I don't think that distance can be made smaller than 1/2^(n-2) in general (in particular, not for a = 3/4 and n = 7). Sep3 comment Game involving points on $[0,1]$ It seems to me that (0, ..., 0, a, 1) is harder for general a than a = 0, so 2^(-n+2) should not be sharp. Mar7 revised How to ensure Topological Correctness equal linking numbers != equivalent links Mar7 suggested approved edit on How to ensure Topological Correctness Mar7 comment How to ensure Topological Correctness @KevinCarlson ah yes - I forgot about this. However it seems solving that problem would be asking for (at least) ways of distinguishing the unknot, which I think is difficult. Dec6 awarded Nice Question Nov6 revised Vague question about polynomials and symmetry f(x,y)->f(y,x) Nov5 asked Vague question about polynomials and symmetry Jul17 asked Fundamental domain of $\operatorname{GL}(n,\mathbb R)$ acted on by $\operatorname{GL}(n, \mathbb Z)$ Jul7 awarded Editor Jul7 revised Symmetric functions of the eigenvalues of A+B, A, B, ABA, BAB, et.c. / /k! Jul7 comment What about other symmetric functions of the eigenvalues? Fair enough. math.stackexchange.com/questions/167978 Jul7 asked Symmetric functions of the eigenvalues of A+B, A, B, ABA, BAB, et.c. Jul7 comment What about other symmetric functions of the eigenvalues? @QiaochuYuan : I would be interested in unclosing this question, since there are generalizations which are not of the kind you mention in your old answer. For example, $i_2(A+B) = i_2(A)+i_2(B) +i_1(A)i_1(B) - i_1(AB)$. This can be found just by comparing coefficients of det(I+tX) for various X, but I have not found a 'unified' answer (expressing the analogous thing for i_k(A+B) in a conceptual way). Jun3 awarded Supporter Jun3 comment What about other symmetric functions of the eigenvalues? Thanks for your answer (the old one in particular)! Jun3 awarded Student Jun3 asked What about other symmetric functions of the eigenvalues?