This page collects my published work, including research in mathematics and computer science, software and more.

Blog Math / CS Economics Software Philosophy Teaching Community Video Fiction

# Blog

On my **personal blog** I write about all kinds of things that interest me. The latest posts are shown on the right.

# Mathematics and Computer Science

Here is a list of my formal research publications. Note that on publications in mathematics, authors are always listed alphabetically.

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**Polyhedral geometry, supercranks, and combinatorial witnesses of congruences for partitions into three parts** (2015) with Dennis Eichhorn and Brandt Kronholm

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**A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins** (2015) with Brandt Kronholm

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**Polyhedral Omega: A New Algorithm for Solving Linear Diophantine Systems** (2015) with Zafeirakis Zafeirakopoulos

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**An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics** (2015)

Felix Breuer,
*An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics*. In: Computer Algebra and Polynomials; Jaime Gutierrez, Josef Schicho, Martin Weimann, editors. Lecture Notes in Computer Science 8942, 1-29, 2015.

Article at SpringerLink Preprint at arXiv

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**Scheduling Problems** (2014) with Caroline J. Klivans

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**Enumerating Colorings, Tensions and Flows in Cell Complexes** (2014) with Matthias Beck, Logan Godkin and Jeremy Martin

Matthias Beck, Felix Breuer, Logan Godkin, Jeremy L. Martin,
*Enumerating colorings, tensions and flows in cell complexes*,
Journal of Combinatorial Theory, Series A **122**(4), 82-106, 2014.

Article at ScienceDirect, Preprint at arXiv

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**Analytic Feature Selection for Support Vector Machines** (2013) with Carly Stambaugh and Hui Yang

Carly Stambaugh, Hui Yang, Felix Breuer,
*Analytic Feature Selection for Support Vector Machines*.
In: Machine Learning and Data Mining in Pattern Recognition; Petra Perner, editor.
Lecture Notes in Computer Science 7988, 219-233, 2013.

Article at SpringerLink, Article at arXiv

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**Ehrhart f*-coefficients of polytopal complexes are non-negative integers** (2012)

Felix Breuer, *Ehrhart f*-coefficients of polytopal complexes are non-negative integers*, Electronic Journal of Combinatorics **19**(4), P16, 2012.

Article at EJC, Preprint at arXiv

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**Hypergraph Coloring Complexes** (2012) with Aaron Dall and Martina Kubitzke

Felix Breuer, Aaron Dall, Martina Kubitzke, *Hypergraph Coloring Complexes*, Discrete Mathematics **312**(16), 2407-2420, 2012.

Article at ScienceDirect, Article at arXiv

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**Ehrhart theory, Modular flow reciprocity, and the Tutte polynomial** (2012) with Raman Sanyal

Felix Breuer, Raman Sanyal, *Ehrhart theory, Modular flow reciprocity, and the Tutte polynomial*, Mathematische Zeitschrift **270**(1), 1-18, 2012.

Article at SpringerLink, Preprint at arXiv

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**Counting Hexagonal Patches and Independent Sets in Circle Graphs** (2012) with Paul Bonsma

Paul Bonsma, Felix Breuer. *Counting Hexagonal Patches and Independent Sets in Circle Graphs*, Algorithmica **63**(3), 645-671, 2012.

Paul Bonsma, Felix Breuer. *Counting Hexagonal Patches and Independent Sets in Circle Graphs*. In: LATIN 2010: Theoretical Informatics; Alejandro López-Ortiz, editor. Lecture Notes in Computer Science Volume 6034, 603-614, 2010.

Journal Article at SpringerLink, Conference Paper at SpringerLink, Preprint at arXiv

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**Bounds on the Coefficients of Tension and Flow Polynomials** (2011) with Aaron Dall

Felix Breuer, Aaron Dall, *Bounds on the Coefficients of Tension and Flow Polynomials*, Journal of Algebraic Combinatorics **33**(3), 465-482, 2011.

Article at SpringerLink, Preprint at arXiv

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**Viewing counting polynomials as Hilbert functions via Ehrhart theory** (2010) with Aaron Dall

Felix Breuer, Aaron Dall. *Viewing counting polynomials as Hilbert functions via Ehrhart theory*. In: 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010). DMTCS, 413-424, 2010.

Article at DMTCS, Poster at FPSAC, Preprint at arXiv

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**Staircases in Z**^{2} (2010) with Frederik von Heymann

^{2}

Felix Breuer, Frederik von Heymann, *Staircases in Z ^{2}*, INTEGERS

**10**, 807-847, 2010.

Article at Integers, Preprint at arXiv

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**Uneven Splitting of Ham Sandwiches** (2010)

Felix Breuer, *Uneven Splitting of Ham Sandwiches*, Discrete and Computational Geometry **43**(4), 876-892, 2010.

Article at SpringerLink, Preprint at arXiv

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**Ham Sandwiches, Staircases and Counting Polynomials** (2009)

PhD Thesis, Freie Universität Berlin, 2009.

Thesis at FU Berlin, Thesis as PDF

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**Finding Fullerene Patches in Polynomial Time** (2009) with Paul Bonsma

Paul Bonsma, Felix Breuer. *Finding Fullerene Patches in Polynomial Time*. In: Algorithms and Computation: 20th International Symposium, ISAAC 2009; Yingfei Dong, Ding-Zhu Du, Oscar Ibarra, editors. Lecture Notes in Computer Science Volume 5878, 750-759, 2009.

Article at SpringerLink, Preprint at arXiv

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**Gauss Codes and Thrackles** (2006)

Diploma Thesis, FU Berlin, 2006.

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**Domino-Pflasterungen und Aztekensterne** (2006) with Daria Schymura

Felix Breuer, Daria Schymura, *Domino–Pflasterungen und Aztekensterne*, Mathematische Semesterberichte **53**(1), 81 - 99, 2006.

Article at SpringerLink, Preprint as PDF

# Economics

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**Fund I/O**

Fund I/O is both: exploratory research and a practical business model. The premise: crowdfunding and novel payment solutions can be used to put theoretical mechanisms for the private provision of public goods to real-world use.

There is no research paper on Fund I/O available yet, but I am keeping an open notebook on both my theoretical findings and practical considerations on my blog. If you want to read more, this is the post to start with. A full list of posts on Fund I/O can be found here.

# Software

I am currently active in the following two software projects.

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**Polyhedral Omega**

Polyhedral Omega is a solver for linear Diophantine systems that I am currently developing with Zafeirakis Zafeirakopoulos. It computes symbolic cone and rational function representations of the set of all integer solutions to a system of linear inequalities. See our paper for details. The current implementation is based on Sage.

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**Substance / Lens**

Substance is a technology stack for reading and writing professional web-first publications. It includes the Lens reader for Substance documents, which is part of the online portals of publishers such as eLife. I am contributing mathematical features to the project.

In the past, I have maintained two open source software projects.

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**Qute**

Qute is a text editor for Windows/Linux/Mac OS built around Markdown and MathJax. It offers TeX support and per-paragraph preview of markup (including typeset formulas)! It also an experiment in the visual aesthetics of text editing. There also is a version of Qute for Android, but that one offers fewer features.

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**InkBoard**

InkBoard is an experimental pen-centric on-screen keyboard which I designed and implemented. It was written in Clojure and is available as open-source software. It is part of the larger InkCode project.

Also, I have been involved in several open source software projects, some of which are worth mentioning.

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**TeXmacs**

TeXmacs is a scientific text editor. I helped implementing the converter to XML formats. I also built a prototype of a literate programming system for TeXmacs, which is still available here.

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**Heretix**

Heretix was a source based GNU/Linux distribution, whose package manager was implemented as a Ruby script. I helped writing packages, maintaining the website and integrating a documentation system into the package manager itself. Heretix has been discontinued.

# Teaching

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**Using Intuitive Geometry** (2011)

In the fall term of 2011 I volunteered to teach Math 890 at San Francisco State University. The title of the course was "Using Intuitive Geometry - Using Geometric Intuition" and it dealt mainly with discrete geometry.

# Community

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**Mathblogging.org**

Along with Peter Krautzberger and Frederik von Heymann, I am one of the co-founders of Mathblogging.org. Mathblogging.org is a blog aggregator for the mathematical blogging community. By providing an index of math blogs, editorial content and technological infrastructure we help readers from any background discover the mathematical blogosphere.

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**Geometry, the Majority Vote and the Power of Agenda Control**

After serious police violence against Occupy protesters in the Bay Area, I joined mathematicians at UC Berkeley in organizing a teach-in. We gave public lectures on mathematical topics with a connection to polictics. I spoke on "Geometry, the Majority Vote and the Power of Agenda Control".

Teach-in, Lecture notes, Video on IndyMedia

# Video

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**Der kleine Gauß** (2010) with Peter Krautzberger

As an experiment in communicating mathematics Peter and I created this video about the intuitive meaning of Gauss' sum formula.

# Philosophy

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**Feldenkrais' Spontaneous Action and Laozi's ***Wuwei* (2012)

*Wuwei*

Felix Breuer, *Feldenkrais' Spontaneous Action and Laozi's Wuwei*, Journal of Daoist Studies

**5**, 169 - 183, 2012.

# Fiction

Now and then I have been writing fiction.

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**Eine inszenierte Revolte** (2007)

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**17 Gen r** (2000)

"17 Gen r" is a fragment of a novel. I brought this project pretty far (beyond 100,000 words), but in the end I did not finish it.

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**Ein Jahr** (1999)

The short story "Ein Jahr" was published in an anthology in 1999.