Exceptional Sequences and Idempotent Functions

2019/09/12 by Emre Sen, Sen, Emre
Mathematics · #05C30 (Secondary) #05E10 #16G20 (Primary) #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1909.05887

openalex publication_date 2019/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that there is a one to one correspondence between the following three sets: idempotent functions on a set of size n, complete exceptional sequences of linear radical square zero Nakayama algebras of rank n and rooted labeled forests with n nodes and height of at most one. Therefore, the number of exceptional sequences is given by the sum ∑ⁿ_j=1\binomnjj^n-j.

Related

• Weak Exceptional Sequences
• On the Number of Exceptional Pairs Over a Class of Nakayama Algebras
• τ-exceptional sequences
• Short history of signed exceptional sequences
• Mutating signed τ-exceptional sequences