Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423930 | Electronic Notes in Discrete Mathematics | 2011 | 6 Pages |
Abstract
Algorithms that compute all finite posets I with a unique maximal element such that the Tits quadratic form qËI:ZIâZ is positive definite are presented. They also determine the Coxeter-Dynkin types of such posets. It is shown that there is one infinite series of the Coxeter-Dynkin type An,n⩾1, three infinite series of type Dn,n⩾4, and a finite set of 193 posets of the Coxeter-Dynkin types E6,E7, and E8. For each such a poset I of the Coxeter-Dynkin type Î, a Z-bilinear equivalence of the bilinear form bI of I with the Euler bilinear form bÎ of the Dynkin diagram Î is presented by computing a Z-invertible matrix B defining the equivalence.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Marcin GÄ
siorek, Daniel Simson,