2010/02/04 by François Bergeron, Bergeron, Francois, Christophe Reutenauer +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1002.1089
openalex publication_date 2010/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study properties of (bi-infinite) arrays having all adjacent k× k adjacent minors equal to one. If we further add the condition that all adjacent (k-1)× (k-1) minors be nonzero, then these arrays are necessarily of rank k. It follows that we can explicit construct all of them. Several nice properties are made apparent. In particular, we revisit, with this perspective, the notion of frieze patterns of Coxeter. This shed new light on their properties. A connexion is also established with the notion of T-systems of Statistical Physics.