{"docId":9535,"paperId":9535,"url":"https:\/\/cm.episciences.org\/9535","doi":"10.2478\/cm-2021-0016","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":648,"name":"Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in M\u00e1laga)"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03665022","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-03665022v1","dateSubmitted":"2022-05-11 15:42:39","dateAccepted":null,"datePublished":"2021-07-15 00:00:00","titles":{"en":"Gradedness of the set of rook placements in An\u22121"},"authors":["Ignatev, Mikhail V."],"abstracts":{"en":"A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system. Degenerations of such orbits induce a natural partial order on the set of rook placements. We study combinatorial structure of the set of rook placements in An\u2212 1 with respect to a slightly different order and prove that this poset is graded."},"keywords":[["General Mathematics"],"[MATH]Mathematics [math]"]}