[{"page":"143-158","citation":{"mla":"Abels, Herbert. “The geometry of the chamber system of a semimodular lattice”. *Order. A Journal on the Theory of Ordered Sets and its Applications* 8.2 (1991): 143-158.","bio1":"Abels H (1991)

The geometry of the chamber system of a semimodular lattice.

Order. A Journal on the Theory of Ordered Sets and its Applications 8(2): 143-158.","apa":"Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. *Order. A Journal on the Theory of Ordered Sets and its Applications*, *8*(2), 143-158. doi:10.1007/BF00383400","frontiers":"Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. *Order. A Journal on the Theory of Ordered Sets and its Applications* 8, 143-158.","ieee":" H. Abels, “The geometry of the chamber system of a semimodular lattice”, *Order. A Journal on the Theory of Ordered Sets and its Applications*, vol. 8, 1991, pp. 143-158.","dgps":"Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. *Order. A Journal on the Theory of Ordered Sets and its Applications*, *8*(2), 143-158. KLUWER ACADEMIC PUBL. doi:10.1007/BF00383400.

","chicago":"Abels, Herbert. 1991. “The geometry of the chamber system of a semimodular lattice”. *Order. A Journal on the Theory of Ordered Sets and its Applications* 8 (2): 143-158.

","harvard1":"Abels, H., 1991. The geometry of the chamber system of a semimodular lattice. *Order. A Journal on the Theory of Ordered Sets and its Applications*, 8(2), p 143-158.","lncs":" Abels, H.: The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications. 8, 143-158 (1991).","ama":"Abels H. The geometry of the chamber system of a semimodular lattice. *Order. A Journal on the Theory of Ordered Sets and its Applications*. 1991;8(2):143-158.","wels":"Abels, H. (1991): The geometry of the chamber system of a semimodular lattice *Order. A Journal on the Theory of Ordered Sets and its Applications*,8:(2): 143-158.","apa_indent":"Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. *Order. A Journal on the Theory of Ordered Sets and its Applications*, *8*(2), 143-158. doi:10.1007/BF00383400

","angewandte-chemie":"H. Abels, “The geometry of the chamber system of a semimodular lattice”, *Order. A Journal on the Theory of Ordered Sets and its Applications*, **1991**, *8*, 143-158.","default":"Abels H (1991)

*Order. A Journal on the Theory of Ordered Sets and its Applications* 8(2): 143-158."},"publisher":"KLUWER ACADEMIC PUBL","user_id":"67994","title":"The geometry of the chamber system of a semimodular lattice","volume":8,"publication":"Order. A Journal on the Theory of Ordered Sets and its Applications","date_updated":"2019-05-03T14:18:14Z","status":"public","department":[{"_id":"10020"}],"_id":"1648931","language":[{"iso":"eng"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"In this paper geometric properties of the following metric space C are studied. Its elements are called chambers and are the maximal chains of a semimodular lattice X of finite height and its metric d is the gallery distance. We show that X has many properties in common with buildings. More specifically, Tits [17] has recently described buildings in terms of \"Weyl-group valued distance functions\". We consider the Jordan-Holder permutation pi(C, D) corresponding to a pair C, D of chambers and show that it has most properties of such a distance with values in the symmetric group."}],"intvolume":" 8","isi":1,"external_id":{"isi":["A1991GT45300004"]},"publication_status":"published","date_created":"2010-04-29T13:30:39Z","article_type":"original","keyword":["WEIL-GROUP VALUED DISTANCE FUNCTION","JORDAN-HOLDER PERMUTATION","SEMIMODULAR LATTICE","SCHUBERT SYMBOL","CHAMBER SYSTEM"],"type":"journal_article","publication_identifier":{"issn":["0167-8094"]},"doi":"10.1007/BF00383400","year":"1991","author":[{"id":"10478","last_name":"Abels","first_name":"Herbert","full_name":"Abels, Herbert"}],"issue":"2"}]