9,018 reputation
1823
bio website math.tulane.edu/~mjoyce3
location New Orleans, LA, USA
age 36
visits member for 2 years, 6 months
seen 2 hours ago

I am interested in algebraic combinatorics related to Schubert calculus and the geometry of spherical varieties.


Apr
10
answered Deriving a (tricky, I think?) recurrence relation
Apr
9
asked Classroom enhancement resources for linear algebra
Apr
9
comment Pi in combinatorial game theory
Well $a_n < \pi$ because, by construction, $c_n < 2^n \pi$, so $a_n = c_n / 2^n < \pi$. But also, by the choice of $c_n$, we have that $c_n + 1 > 2^n \pi$ (otherwise $c_n$ would not be the largest integer less than $2^n \pi$!), so $a_n > \pi - 1/2^n$. Since $\pi - 1/2^n < a_n < \pi$, by the squeeze theorem, $\lim\limits_{n \rightarrow \infty} a_n = \pi$.
Apr
9
comment What area of Abstract Algebra do you find most interesting?
This should be community wiki ...
Apr
9
revised What area of Abstract Algebra do you find most interesting?
edited body
Apr
9
answered What area of Abstract Algebra do you find most interesting?
Apr
9
answered Pi in combinatorial game theory
Apr
4
comment Proof of Nonnegative Determinant
$\det(A + B) \neq \det(A) + \det(B)$!
Apr
2
comment Ordinary Generating functions for $b_n$
A word of advice: any time you write an identity of power series, it is a good idea to check and make sure the coefficients of $x^n$ are the same on both sides for small values of $n$. You'll likely spot your errors (pointed out by Alex) that way. (+1 for showing the work on your problem)
Apr
2
comment Prove it is possible to pick 11 integers whose sum is divisible by 11
There are many ways to interpret your problem. The first thing you need to do is to make sure you understand what is being asked of you. Are you given a set $S$ of $11$ integers and asked to prove that for all such sets $S$ that it is always possible to pick a subset $T$ of $S$ so that the sum of all the elements in $T$ is a multiple of $11$?
Apr
2
comment What means: is equivalent to?
What is $\lambda$? I don't know about the content of the theorem, but a common equivalence relation on functions when studying measure theory is to define $f$ to be equivalent to $g$ if $f(x) = g(x)$ for all $x$ in a set whose complement has measure zero (often referred to as $f = g$ almost everywhere).
Apr
2
comment A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$
The definition of a valuation is available at en.wikipedia.org/wiki/Valuation_%28algebra%29. That will get you started. Can you show that $\nu(fg) = \nu(f) + \nu(g)$? Note that in your definition of $\nu$, the minimum that you are taking should range over all pairs $(n,m)$ such that $c_{n,m} \neq 0$.
Apr
2
comment How to integrate $\int_{1}^{3} {\frac{x^2 - 1}{x^4 + 1}}\, dx$
+1 for a nicely explained computation. Is there any intuition (something one could see before carrying out the computation) as to why you get logarithms, i.e. why the partial fraction decomposition for this particular fraction works out so that each resulting fraction has the numerator equal to the derivative of the denominator, up to a constant factor?
Apr
2
answered Proving $G$ is a group under a specific operation
Apr
2
revised Proving $G$ is a group under a specific operation
fixed LaTeX; corrected grammar
Apr
2
revised Discrete Math on Functions as bijection
fixedd LaTeX
Apr
2
comment Discrete Math on Functions as bijection
Can you think of an inverse function?
Apr
2
revised Congruence and modular arithmetic
fixed LaTeX; corrected grammar; added tags
Apr
2
comment Congruence and modular arithmetic
What is $t$ in this problem?
Mar
27
comment Matrix with determinant 0
If the original version of a question needs to be improved, it is preferred that you edit the original version rather than deleting the first version and posting the question a second time.