Collaborative Research: SI2-SSE: Sage-Combinat: Developing and Sharing Open Source Software for Algebraic Combinatorics

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Sage is an open source general purpose mathematical software system that has developed explosively within the last six years. Sage-Combinat is a subproject whose mission is "to improve Sage as an extensible toolbox for computer exploration in (algebraic) combinatorics, and foster code sharing between researchers in this area". There is a long tradition of software packages for algebraic combinatorics. These have been crucial in the development of combinatorics since the 1960s. The originality of the Sage-Combinat project lies in successfully addressing the following simultaneous objectives. It offers a wide variety of interoperable and extensible tools, integrated in a general purpose mathematical software package, as needed for daily computer exploration in algebraic combinatorics; it is developed by a community of researchers spread around the world and across institutions; and it is open source and depends only on open source software. Among the proposers, Stein is founder and lead developer of Sage while Bump, Musiker, and Schilling are strong contributors to Sage-Combinat. Hivert and Thi´ery (Paris-Sud, Orsay), founders and lead developers of Sage-Combinat, are both strongly affiliated with this project. Some of the research areas addressed in this project include symmetric functions, in particular Macdonald polynomials for arbitrary Cartan types and their nonsymmetric analogues, crystals, rigged configurations and combinatorial R-matrices, affine Weyl groups and Hecke algebras, cluster algebras, and posets. The project will develop Sage-Combinat in areas relevant to the ongoing research of the participants, together with relevant underlying infrastructure. The project will include three Sage Days workshops, and will be affiliated with a third scheduled workshop at ICERM. These workshops include a strong outreach component and have been a potent tool for connecting researchers and recruiting Sage users and developers. The grant will also fund a dedicated software development and computation server for Sage-Combinat, to be hosted in the Sage computation farm in Seattle. Emphasis will be placed on the development of thematic tutorials that will make the code accessible to new users. The proposal will also fund graduate student RA support, curriculum development, and other mentoring.