2022/04/28 by Eirini Chavli, René Marczinzik, Chavli, Eirini +1
Mathematics · #16G10 #18G20 #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.2204.13764
openalex publication_date 2022/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Linear Nakayama algebras over a field K are in natural bijection to Dyck paths and Dyck paths are in natural bijection to 321-avoiding bijections via the Billey-Jockusch-Stanley bijection. Thus to every 321-avoiding permutation π we can associate in a natural way a linear Nakayama algebra Aπ. We give a homological interpretation of the fixed points statistic of 321-avoiding permutations using Nakayama algebras with a linear quiver. We furthermore show that the space of self-extension for the Jacobson radical of a linear Nakayama algebra Aπ is isomorphic to K^\mathfraks(π), where \mathfraks(π) is defined as the cardinality k such that π is the minimal product of transpositions of the form si=(i,i+1) and k is the number of distinct si that appear.