# Per Alexandersson

## Me

OCRID: 0000-0003-2176-0554.

ArXiv: alexandersson_p_1.

MathOverflow: per-alexandersson

## Popular quicklinks

Linear Algebra I - A collection of exercises and solution aimed for the first semester.

Linear Algebra II - A collection of exercises and solution aimed for the course Linear Algebra II.
Here is a phone version.

Linear Algebra for teachers - A collection of exercises and solution plus some short notes on theory.
Here is a phone version.

Combinatorics and counting - A collection of exercises and solution.

Group theory - A collection of exercises and solution.

# About me

Since February 2017, I am working as a postdoc with Svante Linusson at KTH (Stockholm).

Before that, (2015-2017) I worked as a postdoc at University of Pennsylvania, with Jim Haglund, funded by a grant from the Knut and Alice Wallenberg foundation. In 2014, I worked as a postdoc at Universität Zurich, Schweiz with Valentin Féray.

My field of research is representation theory and combinatorics, more specifically, polynomials given by structure constants (Kostka-coefficients, characters of the symmetric group) and Jack generalizations of these, as well as chromatic symmetric functions, LLT polynomials and so on.

In Spring 2013 I defended my thesis titled Combinatorial Methods in Complex Analysis, where Boris Shapiro was my primary advisor. My research interests are mainly combinatorics, complex analysis and algebraic geometry. My favorite research tools are Mathematica, OEIS, FinstStat, MathOverflow and WolframAlpha.

I am also a bit interested in special polynomials, for example real-rooted polynomials and polynomials obtained from combinatorial statistics.

Finally, I must admit that I have a soft spot for tilings, discrete dynamical systems, machine learning, neural networks and cellular automata.

## Symmetric functions database

Want a quick overview of symmetric functions and their generalizations? See this database that I sometimes add things to.

# List of papers

1. (w. Robin Sulzgruber) P-partitions and p-positivity, (arxiv)
2. (w. Linus Jordan) Enumeration of border-strip decompositions, (arxiv)
3. (w. Jim Haglund and George Wang) On the Schur expansion of Jack polynomials, (FPSAC abstract) (arxiv)
4. (w. Nima Amini) The Cone of Cyclic Sieving Phenomena, (submitted) (arxiv)
5. (w. Mehtaab Sawhney) Properties of non-symmetric Macdonald polynomials at $q=0$ and $q=1$, (submitted) (arxiv)
6. (w. Greta Panova) LLT polynomials, chromatic quasisymmetric functions and graphs with cycles, Dicrete Mathematics 341, No.12 (2018) 3453–3482
7. (w. Mehtaab Sawhney) A major-index preserving map on fillings, Electronic Journal of Combinatorics 24, No.4 (2017)
8. Polytopes and large counterexamples, Experimental Mathematics, (2017) 1–6
9. Non-symmetric Macdonald polynomials and Demazure-Lusztig operators, (submitted), (arxiv)
10. (w. V. Féray) Shifted symmetric functions and multirectangular coordinates of Young diagrams, Journal of Algebra 483 (2017), 262–305
11. Polynomials defined by tableaux and linear recurrences, Electronic Journal of Combinatorics 23, No.1 (2016)
12. Gelfand–Tsetlin polytopes and the integer decomposition property, European Journal of Combinatorics, 54, (2016)
13. A combinatorial proof the skew K-saturation theorem, Discrete Mathematics 338 No.1 (2015), 93–102
14. (w. B. Shapiro) Around Mutlivariate Schmidt-Spitzer Theorem, Linear Algebra and its Applications 446 (2014), 356–368
15. Stretched skew Schur polynomials are recurrent, Journal of Combinatorial Theory, Series A 122 (2014) 1–8.
16. Schur polynomials, banded Toeplitz matrices and Widom's formula, Electronic Journal of Combinatorics 19, No.4 (2012)
17. (w. B. Shapiro) Discriminants, symmetrized graph monomials, and sums of squares, Experimental Mathematics 21 No. 4 (2012) 353–361
18. On eigenvalues of the Schrödinger operator with an even complex-valued polynomial potential, CMFT 12 No.2 (2012) 465–481
19. (w. A. Gabrielov) On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential, CMFT 12 No.1 (2012) 119–144

# Other projects

In my spare time, I tinker a bit with a flame fractal renderer written in Java. You can browse the source on Sourceforge.