Sobre el número de pares excepcionales en carcajes de tipo A_n

Abstract

In the context of path algebras of a quiver Q the exceptional sequences were introduced by Crawley-Boevey in 1992, these sequences are sequences of representations of a quiver which satisfies some homological properties. For a given length, compute the number of exceptional sequences for any quiver Q can be a tricky problem in representation theory and combinatorics. However, if Q is a Dynkin diagram of type A_n and the length is n the description was given by Seidel in 2001 and Araya in 2009. In this work combinatorial and homological tools are used in order to describe and enumerate the exceptional pairs (exceptional sequences of length two) when Q is a Dynkin diagram of type A_n, in order to produce a categorification in the sense of Ringel and Fahr of the sequence A004320 in the OEIS (The On-line Encyclopedia of Integer Sequences).