Selected non-holonomic functions in lattice statistical mechanics and enumerative combinatorics

Statistical Mechanics and Combinatorics of Some Discrete Lattice Models

OF THE DISSERTATION Statistical Mechanics and Combinatorics of Some Discrete Lattice Models by Arvind Ayyer Dissertation Director: Professor Joel L. Lebowitz Many problems in statistical physics involve enumeration of certain objects. In this thesis, we apply ideas from combinatorics and statistical physics to understand three different lattice models. I We investigate the structure of the none...

Combinatorics Enumerative Combinatorics 05

Enumerative and Algebraic Combinatorics

Enumeration, alias counting, is the oldest mathematical subject, while Algebraic Combinatorics is one of the youngest. Some cynics claim that Algebraic Combinatorics is not really a new subject but just a new name given to Enumerative Combinatorics in order to enhance its (former) poor image, but Algebraic Combinatorics is in fact the synthesis of two opposing trends: abstraction of the concret...

NSF Proposal: Automated Enumerative Combinatorics Automated Enumerative Combinatorics

My research students and I continued to practice a new research methodology, that can be loosely called rigorous experimental mathematics. It has something in common with both “mainstream” experimental mathematics (as preached by the Borwein brothers, David Bailey, Victor Moll, and their collaborators, see e.g. the masterpiece [BB], and the recent collection [BBCGLM]), and automated theorem pro...

Enumerative Combinatorics 8: Species

In this lecture I will discuss a very nice unifying principle for a number of topics in enumerative combinatorics, the theory of species, introduced by André Joyal in 1981. Species have been used in areas ranging from infinite permutation groups to statistical mechanics, and I can’t do more here than barely scratch the surface. Joyal gave a category-theoretic definition of species; I will take ...