Arvind Ayyer

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I extensively use mathematical experimentation as part of my research. I mainly use a mixture of Maple, Mathematica and Sage.
In particular, I regularly write programs which either directly solve or help me solve problems. Here are some of them in reverse chronological order, along with the accompanying papers.
I have slowly started contributing to Sage.

Maple programs

• RandomJuggling - We study probabilistic models of juggling in this paper. The package contains programs for Markov chains on juggling configurations and set partitions.
• ToomTsetlin - In this survey article written jointly with Anne Schilling, Benjamin Steinberg and Nicolas M. Thiéry, we introduced two new generalizations of the Tsetlin library which allow for multiple copies of books.
  Formulas for the spectra of transition matrices in both cases can be verified using the programs here.
• Monopole - Verifies the determinant formulas for the loop-vertex model and the monopole-dimer model in this paper.
• NonabelianSandpiles - With Anne Schilling, Benjamin Steinberg and Nicolas M. Thiéry, we proved results about a class of nonabelian sandpile models on directed trees in this paper. Sage was also extensively used in this project.
• InhomTasep - With Svante Linusson, I considered the multispecies TASEP on the ring with inhomogeneous rates in this paper.
• LinearExtensions - With Steven Klee and Anne Schilling, I considered some combinatorial Markov chains for linear extensions of posets in this paper. Sage was also extensively used in this project.
• RefinedASM1234 - With Dan Romik, I looked at refined enumeration for alternating sign matrices in this paper. We also verified a claim of Colomo and Pronko stated in the paper in this mathematica file.
• RS - For studying the Razumov-Stroganov conjecture using Alternating Paths for this paper. A package written by Doron Zeilberger for the same study is FPL.
• Ferrers - Umbral operators for Wicketed and Gated Ferrrers diagrams. All the assertions of this paper can be checked here.
• TASEP - Basic analysis of different kinds of totally asymmetric simple exclusion processes - open, closed and restricted. Calculates steady state probabilities, densities and two point correlations.
• POLYMER - Analysis of directed walks (as models of polymers) in a strip of arbitrary finite size as well as the infinite quarter plane. It calculates quantities of mathematical interest such as generating functions as well as those of physical interest such as the free energy and the force exerted by the polymers. It is an integral part of this paper.
• Guessdiff - A package which guess various properties of tilings (with an arbitrary set of tiles) in the plane using the TILINGS package of Doron Zeilberger. This was written for Math 640 in Spring 2006.