{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825491,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Linear Nakayama algebras over a field $K$ are in natural bijection to Dyck paths and Dyck paths are in natural bijection to 321-avoiding permutations via the Billey-Jockusch-Stanley bijection. Thus to every 321-avoiding permutation $\\pi$ we can associate in a natural way a linear Nakayama algebra $A_{\\pi}$.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-extensions for the Jacobson radical of a linear Nakayama algebra $A_{\\pi}$ is isomorphic to $K^{\\mathfrak{s}(\\pi)}$, where $\\mathfrak{s}(\\pi)$ is defined as the cardinality $k$ such that $\\pi$ is the minimal product of transpositions of the form $s_i=(i,i+1)$ and $k$ is the number of distinct $s_i$ that appear.<\/jats:p>","DOI":"10.37236\/13107","type":"journal-article","created":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T16:25:47Z","timestamp":1738254347000},"source":"Crossref","is-referenced-by-count":0,"title":["Homological Algebra of Nakayama Algebras and 321-Avoiding Permutation"],"prefix":"10.37236","volume":"32","author":[{"given":"Eirini","family":"Chavli","sequence":"first","affiliation":[]},{"given":"Rene","family":"Marczinzik","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2025,1,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T16:25:47Z","timestamp":1738254347000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i1p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1,17]]}},"URL":"https:\/\/doi.org\/10.37236\/13107","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,1,31]]},"article-number":"P1.13"}}