Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs

Applications in Enumerative Combinatorics of Infinite Weighted Automata and Graphs

In this paper, we present a general methodology to solve a wide variety of classical lattice path counting problems in a uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted automata, equations of ordinary generating functions and continued fractions. This new methodology is called Counting Automata Methodology. It...

Weighted Automata and Logics on Infinite Graphs

We show a Büchi-like connection between graph automata and logics for infinite graphs. Using valuation monoids, a very general weight structure able to model computations like average or discounting, we extend this result to the quantitative setting. This gives us the first general results connecting automata and logics over infinite graphs in the qualitative and the quantitative setting.

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...