Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/43347
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dc.contributor.authorLunts, Valery-
dc.contributor.authorSPENKO, Spela-
dc.contributor.authorVAN DEN BERGH, Michel-
dc.date.accessioned2024-07-09T06:28:16Z-
dc.date.available2024-07-09T06:28:16Z-
dc.date.issued2024-
dc.date.submitted2024-07-09T05:36:26Z-
dc.identifier.citationPure and Applied Mathematics Quarterly, 20 (3) , p. 1433 -1458-
dc.identifier.urihttp://hdl.handle.net/1942/43347-
dc.description.abstractWe find an explicit S-n -equivariant bijection between the integral points in a certain zonotope in R- n , combinatorially equivalent to the permutahedron, and the set of m-parking functions of length n. This bijection restricts to a bijection between the regular S n -orbits and (m, n)-Dyck paths, the number of which is given by the Fuss-Catalan number A( n) (m, 1). Our motivation came from studying tilting bundles on noncommutative Hilbert schemes. As a side result we use these tilting bundles to construct a semi-orthogonal decomposition of the derived category of noncommutative Hilbert schemes.-
dc.description.sponsorshipWe thank Cesar Ceballos for very helpful discussions, in particular for teaching us about parking functions which lead to the simple proof of Corollary 1.6. We further thank him for making us aware of a plethora of incarnations and variations of Catalan numbers and for providing references. While this work was in its final stages, the second author attended Tudor P ˘a durariu’s interesting lecture in the workshop “Representation theory and flag or quiver varieties” (Paris, June 2022) during which he reported on joint We thank Cesar Ceballos for very helpful discussions, in particular for teaching us about parking functions which lead to the simple proof of Corollary 1.6. We further thank him for making us aware of a plethora of incarnations and variations of Catalan numbers and for providing references. While this work was in its final stages, the second author attended Tudor P ˘a durariu’s interesting lecture in the workshop “Representation theory and flag or quiver varieties” (Paris, June 2022) during which he reported on joint-
dc.language.isoen-
dc.publisherINT PRESS BOSTON, INC-
dc.titleCatalan numbers and noncommutative Hilbert schemes-
dc.typeJournal Contribution-
dc.identifier.epage1458-
dc.identifier.issue3-
dc.identifier.spage1433-
dc.identifier.volume20-
local.format.pages26-
local.bibliographicCitation.jcatA1-
dc.description.notesLunts, V (corresponding author), Indiana Univ Bloomington, Dept Math, Rawles Hall 251,831 East 3rd St, Bloomington, IN 47405 USA.; Lunts, V (corresponding author), Natl Res Univ, Higher Sch Econ, Moscow, Russia.-
dc.description.notesvlunts@indiana.edu; spela.spenko@ulb.be; michel.vandenbergh@uhasselt.be-
local.publisher.placePO BOX 43502, SOMERVILLE, MA 02143 USA-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.identifier.isi001249479000011-
local.provider.typewosris-
local.description.affiliation[Lunts, Valery] Indiana Univ Bloomington, Dept Math, Rawles Hall 251,831 East 3rd St, Bloomington, IN 47405 USA.-
local.description.affiliation[Lunts, Valery] Natl Res Univ, Higher Sch Econ, Moscow, Russia.-
local.description.affiliation[Spenko, Spela] Univ Libre Bruxelles, Dept Math, Campus Plaine CP 213,Blvd Triomphe, B-1050 Brussels, Belgium.-
local.description.affiliation[van den Bergh, Michel] Univ Hasselt, Vakgroep Wiskunde, Univ Campus, B-3590 Diepenbeek, Belgium.-
local.description.affiliation[van den Bergh, Michel] Vrije Univ Brussel, Dept Math & Data Sci, Pl Laan 2, B-1050 Brussels, Belgium.-
local.uhasselt.internationalyes-
item.fullcitationLunts, Valery; SPENKO, Spela & VAN DEN BERGH, Michel (2024) Catalan numbers and noncommutative Hilbert schemes. In: Pure and Applied Mathematics Quarterly, 20 (3) , p. 1433 -1458.-
item.contributorLunts, Valery-
item.contributorSPENKO, Spela-
item.contributorVAN DEN BERGH, Michel-
item.fulltextWith Fulltext-
item.accessRightsOpen Access-
crisitem.journal.issn1558-8599-
crisitem.journal.eissn1558-8602-
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