On the Number of Exceptional Pairs Over a Class of Nakayama Algebras
Pedro Fernando Fern\'andez Espinosa, David Reynoso-Mercado
TL;DR
This paper provides explicit formulas for counting exceptional pairs in certain Nakayama Algebras and explores their connection with integer sequences, using combinatorial and homological methods.
Contribution
It introduces new combinatorial formulas for exceptional pairs in Nakayama Algebras and links these counts to OEIS integer sequences.
Findings
Explicit formulas for exceptional pairs in Nakayama Algebras
Connection between exceptional pairs and OEIS sequences
Homological tools used for combinatorial enumeration
Abstract
In this paper some combinatorial and homological tools are used to describe and give an explicit formula for the number of exceptional pairs (exceptional sequences of length two) for some classes of Nakayama Algebras and for the Auslander algebra of a radical square zero algebra of type . In addition, we explore how the number of exceptional pairs can be connected with some integer sequences in the OEIS (The On-line Encyclopedia of Integer Sequences).
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