Reputation
24,743
Next privilege 25,000 Rep.
Access to site analytics
Badges
22 71
Newest
 Nice Answer
Impact
~315k people reached

3h
comment Can we always attain another prime via inserting digits between the digits of a fixed prime?
At least for $n \le 10^5$, it always suffices to insert one digit in each position.
1d
comment Computing the inverse of a Cholesky decomposition
That's the best I have to offer. The map from the Cholesky decomposition of $A$ to that of $A^{-1}$ does not appear to be simple.
1d
answered Computing the inverse of a Cholesky decomposition
Feb
4
revised Divergence of general random series and a special case
added 71 characters in body
Feb
4
comment Divergence of general random series and a special case
@AnthonyQuas You can exceed lower bounds, but not all conditions are lower bounds.
Feb
4
answered Divergence of general random series and a special case
Feb
3
comment Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
i.e. multiply Tony's equation by $x^n$, sum for $n=1 \ldots \infty$ (interchanging the order of summations) and add $1$, and you should get $$g(x) = \dfrac{x}{1-4x} + \dfrac{x g(x)}{1-x} + \dfrac{x^2 g(x)}{1-5x+4x^2}$$ where $g(x)$ is the g.f. Solve: $$ g(x) = \dfrac{1-4x+3x^2}{1-6x+7x^2}$$
Feb
2
comment Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
You should be able to get the g.f. from Tony Huynh's recursion equation, and it follows from that.
Feb
2
revised Trying to solve this non-linear differential equation
added 121 characters in body
Feb
2
revised Trying to solve this non-linear differential equation
added 719 characters in body
Feb
2
answered Trying to solve this non-linear differential equation
Feb
2
comment Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
Sorry, mistake in my program, corrected. Actually you want $f(2,2)=8$.
Feb
2
revised Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
edited body
Feb
2
revised Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
edited body
Feb
2
answered Number of ways of tiling a $2 \times n$ rectangle using rectangles with integer sides
Feb
2
answered Integral transforms involving square roots
Feb
2
answered Unfamiliar prime-generating polynomials related to Heegner numbers
Jan
29
revised Extracting a full rank matrix from a 0-1 matrix
deleted 2 characters in body
Jan
29
comment Extracting a full rank matrix from a 0-1 matrix
In principle yes: if you want the coefficient of $X^k$ you could work in a quotient ring mod the ideal $\langle X^{k+1}\rangle$. In practice, at least if using Maple, I suspect you're unlikely to beat the performance of CharacteristicPolynomial in the LinearAlgebra[Modular] package, which computes the whole characteristic polynomial mod $p$, unless perhaps $n$ is very large compared to $k$.
Jan
29
comment Techniques for the analysis of interacting particle systems with a finite number of particles, which do not resort to limiting arguments?
For example, you might look at the Wikipedia article n-body choreography and references given there.