{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:56:16Z","timestamp":1776783376519,"version":"3.51.2"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2002,10]]},"abstract":"<jats:p>This article is devoted to the study of several algebras related to symmetric functions, which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young tableaux (free symmetric functions) and packed integer matrices (matrix quasi-symmetric functions). Free quasi-symmetric functions provide a kind of noncommutative Frobenius characteristic for a certain category of modules over the 0-Hecke algebras. New examples of indecomposable H<jats:sub>n<\/jats:sub>(0)-modules are discussed, and the homological properties of H<jats:sub>n<\/jats:sub>(0) are computed for small n. Finally, the algebra of matrix quasi-symmetric functions is interpreted as a convolution algebra.<\/jats:p>","DOI":"10.1142\/s0218196702001139","type":"journal-article","created":{"date-parts":[[2002,10,18]],"date-time":"2002-10-18T09:38:20Z","timestamp":1034933900000},"page":"671-717","source":"Crossref","is-referenced-by-count":117,"title":["NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS"],"prefix":"10.1142","volume":"12","author":[{"given":"G\u00c9RARD","family":"DUCHAMP","sequence":"first","affiliation":[{"name":"Laboratoire d'Informatique Fondamentale et Appliqu\u00e9e de Rouen, Facult\u00e9 des Sciences, Universit\u00e9 de Rouen, 76821 Mont-Saint-Aignan cedex, France"}]},{"given":"FLORENT","family":"HIVERT","sequence":"additional","affiliation":[{"name":"Institut Gaspard Monge, Universit\u00e9 de Marne-la-Vall\u00e9e, 77454 Marne-la-Vall\u00e9e cedex, France"}]},{"given":"JEAN-YVES","family":"THIBON","sequence":"additional","affiliation":[{"name":"Institut Gaspard Monge, Universit\u00e9 de Marne-la-Vall\u00e9e, 77454 Marne-la-Vall\u00e9e cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_3","first-page":"569","volume":"275","author":"Comtet L.","year":"1972","journal-title":"Paris, Ser. 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