# Homepage of Jan Snellman

## Homepage of Jan Snellman

## How to reach me

### Office

Room 659, corridor A, floor 1, house B.

*Office phone*

+46 (0)13 28 1444

**jan.snellman@liu.se**

### Regular mail

- Jan Snellman
- Matematiska Institutionen
- Linköpings Universitet
- 581 83 Linköping
- Sweden

## Career

### PhD studies

I was a PhD student at Stockholm University under the supervision of Jörgen Backelin. I was also advised and tutored by Jan-Erik Roos and Ralf Fröberg.

Other professors that helped broaden my horizons were Clas Löfwall and Torsten Ekedahl.

Fellow PhD-students in the commutative algebra group were Emil Sköldberg, Kristina Crona, and Freyja Hreinsdóttir.

I shared office with fellow PhD-students Ozan Öktem and
Leif Johansson, and took many courses together with them and **Andreas Nilsson**
and Erik Backelin.

I graduated in february 1998, with the thesis A graded subring of an inverse limit of polynomial rings. In brief, my thesis is about Gröbner bases of generic ideals, in “the ring of generalized polynomials”. I studied how initial ideals of sequences of ideals in polynomial rings with ever more variables stabilizes.

### Work at the “radio facility”

Before finishing my PhD I worked for about a year at a goverment agency doing cryptography. I have, sadly, forgotten most of what I learned there.

### Post-doc

I was a post-doc at **Laboratoire GAGE** at Ecole Polytechnique,
Palaiseau, Paris, France, from 1998-10-01 to 1999-09-01. I was funded by
grants from *Centre International des Etudiants et Stagiaires* and
*Svenska Institutet*. Laboratoire GAGE was a CNRS-funded “laboratory” with
about 10 reserchers and 5 phd students. It has since been absorbed by
Laboratoire X.

During the period 1999-10-11 to 2000-07-05 I was at the
**School of Informatics** at the University of Wales, Bangor, supported by grants from KVA
and Svenska Institutet. The school of Informatics has since then been dismantled.

I do not think it is more than a strange coincidence that every department where I was a post-doc has ceased to exist!

### Temporary work at Linköping

The autumn of 2000, and the spring of 2001, and the first half of the autumn of 2001 I taught at the department of mathematics at Linköping University.

### Reserch position at Stockholm

From the autumn of 2002 to the summer of 2005 I held a position as a “forskarassistent” at Stockholm University.

### Permanent teaching position at Linköping

From october 2005 and onwards, I am an assistant professor (swedish “universitetslektor”) at Linköping.

## Research

### Areas of interest

### Articles and preprints

#### Articles

- 2005

**A conjecture on the Poincaré-Betti series of modules of differential operators on a generic hyperplane arrangement**, Experimental Mathematics, vol 14 (2005), no 4, pp 445-456 math.AC/0408437

- 2004

**Standard paths in another composition poset**The electronic journal of combinatorics, volume 11(1) 2004, R76 math.CO/0309458**The ring of arithmetical functions with unitary convolution: Divisorial and topological properties**, Archivum Mathematicum (Brno), tomus 40, 2004/2, pp 161-179. math.RA/0201082, Research Reports in Mathematics 2002/4.**Enumeration of concave integer partitions**, joint work with Michael Paulsen, Journal of Integer Sequences, Vol. 7 (2004), Article 04.1.3, math.CO/0309065

- 2003

**Truncations of the ring of arithmetical functions with unitary convolution**,*International Journal of Mathematics, Game Theory, and Algebra*, 13 (2003), no. 6, 485–519. math.RA/0208183 and math.RA/0205242.**Lifting Gröbner bases from the exterior algebra**,*Communications in Algebra*, vol 31, issue 12, 2003. Joint work with Andreas Nilsson, Paris-Sud, Tokyo, KTH. math.RA/0010117**The maximal spectral radius of a digraph with**(m+1)^{2}- s**edges**, Electronic Journal of Linear Algebra, volume 10 (2003), pp 179-189. math.CA/0210365

- 2002

**Factorisation in topological monoids**,*International Journal of Mathematics, Game Theory, and Algebra,*volume 12, no 4, 2002, pp 313-324. math.GN/9902137**Some conjectures on the Hilbert series of generic ideals in the exterior algebra**, Homology, homotopy and applications, volume 4, no 2, 2002, pages 409-426, math.RA/0007089, joint work with Guillermo Moreno Socías, Versailles.

- 2001

**On the degrees of minimal generators of homogeneous ideals in the exterior algebra**, joint work with Guillermo Moreno Socías, Versailles.*Communications in Algebra*, Vol. 29,#11 (Nov. 2001), pages 5155–5170. MR 1 856 949. ZB pre01690505. Postscript**A poset classifying non-commutative term orders**. Discrete mathematics and theoretical computer science procedings AA (DM-CCG) 2001, pp 301-314. math.CO/0201083, MR 1 88 781. See also the slides from my talk.

- 2000

**Non-homogeneous ideals in a graded subring of the power series ring on a countably infinite number of variables over a field***International Journal of Mathematics, Game Theory, and Algebra,*volume 10, no 5, 2000, pp 391-404. Postscript. MR CMP 1 763 032.**Truncations of the ring of number-theoretic functions**, Homology, homotopy and applications, volume 2, 2000, pages 17-27, math.NT/9904143, MR 1 750 379- *On some partial orders associated to generic initial ideals*, Séminaire Lotharingien de Combinatoire, B43h, 2000, math.CO/9811095, MR 1 756 409

- 1999

*Topological properties of inverse limits of free abelian monoids, with an application to inverse limits of UFDs*. Semigroup Forum volume 59, pp 418-434, 1999. Also available as Postscript. ZB pre990.63115 CMP1847656

Some (minor) errors corrected in

**Correction of two errors in: “Topological properties of inverse limits of free abelian monoids, with an application to inverse limits of UFDs”**. Semigroup Forum 64 (2002), no. 3, 489–490. MR 1 896 383.**Some topological properties of a subring of the power series ring on a countably infinite number of variables over a field***International Journal of Mathematics, Game Theory, and Algebra,*volume 8, no 4, 1999. Postscript. MR CMP1680346. ZB 928.13015

- 1998

**Generalized Hilbert numerators***Communications in Algebra*, volume 27, no 1, 1998. Postscript. MR 99m:13033. ZB 929.13009**Reverse lexicographic initial ideals of generic ideals are finitely generated**In*Gröbner Bases and Applications: Proceedings of the Conference 33 years of Gröbner Bases*, ed Buchberger, B. and Winkler, F., London Mathematical Society Lecture Notes Series, vol 251, 1998. PostScript. ZB 980.34387 MR CMP 1 708 900.**Initial ideals of truncated homogeneous ideals***Communications in Algebra*, 1998, volume 26, number 3. Postscript. MR 99k:13030. ZB 915.13013**Gröbner bases and normal forms in a subring of the power series ring on countably many variables over a field**,*Journal of Symbolic Computation*1998, vol 25, number 3, pp 315-328. Postscript. MR99h:13035. Available from IDEAL. ZB 980.49971

#### Preprints

**Generating functions for borders**, arXiv:0710.5415**On the number of plane partitions and non isomorphic subgroup towers of abelian groups**, joint work with Johan Andersson, arXiv:math/0607698**Laplacians on shifted multicomplexes**, math.CO/0606104**Infinite Minkowski sums of lattice polyhedra**, math.AC/0508092**Saturated Chains in Composition Posets**, Report no 11, 2004/2005,spring,Institut Mittag-Leffler, math.CO/0505262.**Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functions**, math.CO/0211201**Bounds for the entropy of graded algebras**, math.RA/0209080,**Generalised Hilbert Numerators II**, math.RA/0003097

#### PhD Thesis

**A graded subring of an inverse limit of polynomial rings**, consists of
the articles GBN, IIT, RLI, GHN, STP, NHI.
Slightly modified version (errata added)

### Lectures

- Mittag-Leffler talk on posets of termorders
- colloqium talk 2006-03-15
- docentföreläsning 2006-11-21 on lattice points in cones (in swedish)
- talk 2008-12-12 on term orders (in swedish)
- non-commutative term orders
- Laplacians on multicomplexes talk 2009-06-12 at the conference in honor of Ralf Fröbergs 65’th birthday.
- f-vectors of simplicial complexes, talk at Algebra seminar at Linköping, 2023-12-07.

## Supervision

### PhD students

- I was the main supervisor for Jonna Gill, who defended her PhD thesis The k-assignment polytope, phylogenetic trees, and permutation patterns in 2013. For the first half of her studies, Jonna had Svante Linusson as her advisor.
- I was the secondary advisor for Mikael Hansson, who defended his PhD thesis Combinatorics and topology related to involutions in Coxeter groups. Axel Hultman was the main advisor.
- I was similarly the secondary advisor for Vincent Umutabazi, who defended his thesis Boolean complexes of involutions and smooth intervals in Coxeter groups in 2022. Axel Hultman was the main advisor.

### Masters and candidate exams

- Elin Gawell, Rings of arithmetic functions with regular convolutions, 2005, Stockholm University
- Kåre Krig, Methods for phylogenetic analysis 2010.
- Olle Abrahamsson, A Gröbner basis algorithm for fast encoding of Reed-Müller codes, 2016
- Ludwig Rahm, Generating functions and regular languages of walks with modular restrictions in graphs, 2017
- Aliaksandra Kupreyeva, Simplices of f-vectors, 2019