133 reputation
6
bio website none
location Ann Arbor, MI
age 41
visits member for 2 years, 2 months
seen Feb 26 '13 at 1:08

Third year undergraduate in mathematics.


Jun
25
awarded  Teacher
Aug
17
answered Math book for an eager learner with non-mathematical background
Apr
15
comment Weak Dirichlet's theorem for powers of primes
@KCd: The proof where I used Dirichlet's theorem proves it for all $a\in \mathbf{Z}$. You look $\sum_{d|n}\mu(n/d)a^d$ modulo $p^{\operatorname{ord}_p(n)}$. Then it splits into two cases, when $\operatorname{gcd}(p,a)=1$ and otherwise. You can use Dirichlet's theorem for the coprime case, and in the other case, you just follow your nose by looking at when the various Möbius terms vanish.
Apr
14
comment Weak Dirichlet's theorem for powers of primes
@KCd: I was just asking because I was proving the integrality (in general) of Gauss's formula whose value on $q=p^k$ is the the number of irreducible polynomials of degree $m$ in $F_q$. I ended up in a spot where I used Dirichlet's theorem, but I was reluctant to use such powerful technology, which is why I asked if perhaps there was a weaker form of Dirichlet's theorem that I could use instead. It appears that this is not the case.
Apr
14
awarded  Editor
Apr
14
comment Weak Dirichlet's theorem for powers of primes
Ah, thanks. $ $
Apr
14
revised Weak Dirichlet's theorem for powers of primes
added 5 characters in body
Apr
14
asked Weak Dirichlet's theorem for powers of primes
Mar
16
comment Counting the total-order extensions of |2| × |n|
Thanks! I was thinking that perhaps the way to mess with it would be to take the transitive reflexive closure of the relation <, where a<b iff a can be obtained from b by transposing a higher number left past a lower number (assume that the righthand copy of each number lives in a fixed position, then pass a higher number past one of these fixed lower numbers).
Mar
15
comment Counting the total-order extensions of |2| × |n|
dtldarek, wondering: If you look at the set of total extensions of the poset in question, is there an "obvious" partial ordering on this set with maximal element given by the sequence 112233...nn and with minimal element given by the sequence 123...n123...n. I'm modeling the various ways of composing "cubically suspended" strict omega-categories
Mar
15
awarded  Supporter
Mar
13
awarded  Student
Mar
13
awarded  Scholar
Mar
13
accepted Counting the total-order extensions of |2| × |n|
Mar
13
comment Counting the total-order extensions of |2| × |n|
Nifty, thanks! $ $
Mar
13
asked Counting the total-order extensions of |2| × |n|
Jan
29
awarded  Autobiographer