Per Alexandersson

Zurich, Switzerland

www2.math.su.se/~per

Age: 28

Currently interested in Schur functions and semistandard Young tableaux and misc. related representation theory and combinatorics.

Phd thesis defended 2013, titled Combinatorial Methods in Complex Analysis.

I keep an eye out for interesting results related to complex dynamics, computability, and computer-assisted research. I use Mathematica extensively in my research. My other main programming languages are Java, LaTeX, PHP, C, etc.

1d
comment For which sidelengths are there polyominos composed of three squares that tile the plane?
There is a notion of a generalized hexagon, all your examples above are such "hexagons", and these tile the plane.
2d
answered The maximal eigenvalue of a symmetric Toeplitz matrix
Mar
22
comment Determinant of a Vandermonde matrix of roots of monic polynomial with integer coefficients
Ah, right, that's true... was too quick there, haha.
Mar
22
answered Determinant of a Vandermonde matrix of roots of monic polynomial with integer coefficients
Mar
20
accepted Positivity of Ehrhart polynomial coefficients
Mar
20
comment Positivity of Ehrhart polynomial coefficients
@RichardStanley Ah, I suspected that was something about that. I wonder what smallest counter-example there is: There is no $5$-dimensional such order polytope, (checked by computer). I got the conjecture about 01-polytopes from an earlier version of a paper I found online, and the final version does not include this conjecture. If you would make your comment into an answer, I would accept that, since this was really the information I was looking for (but not the answer I was hoping for).
Mar
20
reviewed Approve suggested edit on quadratic matrix equation
Mar
19
reviewed Approve suggested edit on Dual of the space of Hölder continuous functions?
Mar
19
comment Positivity of Ehrhart polynomial coefficients
@RichardStanley: I might be mistaken, but the first poset Figure 3.87 in EC1 2nd ed, gives the inequalities $z \leq x_1 \leq y$, $z\leq x_2$ and $z\leq x_3$ together with the condition that all values are between $0$ and $k$. Asking Mathematica for counting solutions gives the polynomial $\frac{1}{120} (k+1) (k+2) (k+3) \left(12 k^2+33 k+20\right)$. The code I used for counting lattice points: Table[Length@List@ToRules@Reduce[ And[z <= x1 <= y, z <= x2, z <= x3] && And[0<=z<=k,0<=y<=k,0<=x1<=k,0<=x2<=k,0<=x3<= k], {z, y, x1, x2, x3}, Integers],{k, 0, 5}]
Mar
19
comment Reference for multivariate orthogonal polynomials
I recommend this also.
Mar
18
comment Reference for multivariate orthogonal polynomials
Are you looking for representation-theoretical polynomials (Such as Jack, Macdonald, Schur), or of other types (Chebyshev, Koornwinder, Laguerre)?
Mar
17
comment How can find this two sequence recursive relations?
The question, as it stands now, is poorly worded, maybe you can improve it a bit, and provide some more information? Have you tried plugging it in any software? Mathematica can sometimes solve such sums as hypergeometric series.
Mar
16
reviewed Approve suggested edit on Euler-Lagrange Equation and "Eigen Value "
Mar
16
answered What advanced Area of Mathematics can be delved into with only basic Calculus and Linear Algebra
Mar
7
awarded Nice Question
Mar
5
comment Number of Dyck paths with k returns and b peaks
This forum support LaTeX :)
Mar
3
comment Maximizing the number of semistandard Young tableaux
Interesting, this would also, in the limit, maximize the volume of the corresponding Gelfand-Tsetlin polytope, with boundary values given by the restriction on the partitions...
Mar
3
revised Maximizing the number of semistandard Young tableaux
integer -> real number
Mar
3
comment Publication in proceedings
@CarloBeenakker: Computer science has a different approach to publications, where conferences are more important than journal publications.
Mar
2
reviewed Approve suggested edit on Is there a citeable reference for star-shaped open subsets of R^n being diffeomorphic to R^n?
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