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awarded  Good Question
18h
awarded  Nice Question
20h
asked Recent observation of gravitational waves
Feb
9
revised Pragmatic Test for Total Unimodularity
corrected misspelling
Feb
9
answered Pragmatic Test for Total Unimodularity
Feb
5
awarded  Enlightened
Feb
5
awarded  Nice Answer
Feb
4
revised A sum over characters of the symmetric group
sentence addd at end
Feb
4
answered A sum over characters of the symmetric group
Jan
23
answered Generalized cycle index polynomial for the symmetric group
Jan
22
awarded  Enlightened
Jan
22
awarded  Nice Answer
Jan
22
revised Plugging $1-x$ into Schur polynomials
Proof sketch added as an addendum.
Jan
22
comment Log-concave polynomial is a log-concave function?
A stronger condition than log-concave is having only real zeros. Such polynomials are log-concave functions.
Jan
22
answered Plugging $1-x$ into Schur polynomials
Jan
15
comment Characters of permutation groups
One can give a more combinatorial version of this proof. To evaluate $\sum_{(\sigma,k)}x^m$, first choose $k$ in $N$ ways, giving a factor $Nx$. Then choose a permutation on the remaining $N-1$ letters, giving a factor $x(x+1)\cdots (x+N-2)$.
Dec
28
comment How do I evaluate this sum for $s$ is a complex variable :$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{2s}n!}$?
I meant $\int_0^1 \frac{1-e^{-x}}{x}dx$.
Dec
27
comment How do I evaluate this sum for $s$ is a complex variable :$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{2s}n!}$?
Note for instance that $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n\cdot n!} = \int_0^1\frac{e^x-1}{x}dx$, which has no known closed form expression.
Dec
20
comment Is there a short proof that the Kostka number $K_{\lambda \mu}$ is non-zero whenever $\lambda$ dominates $\mu$?
The first proofs of this result are by Lam and Leibler-Vitale. See sciencedirect.com/science/article/pii/0022404977900305.
Dec
20
comment Is there a short proof that the Kostka number $K_{\lambda \mu}$ is non-zero whenever $\lambda$ dominates $\mu$?
Continuing my previous comment, you also cannot fill in the shape by columns, at each step inserting the smallest number possible. E.g., $\lambda=(3,3)$, $\mu=(2,2,2)$.