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A Combinatorial Determinant Dual to the Group Determinant
| Content Provider | Semantic Scholar |
|---|---|
| Author | Srinivasan, Murali K. Mishra, Ashish Kumar |
| Copyright Year | 2015 |
| Abstract | We define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We show that the following combinatorial example is a commuting algebra determinant. Let Bq(n) denote the set of all subspaces of an n-dimensional vector space over Fq. The type of an ordered pair (U, V ) of subspaces, where U, V ∈ Bq(n), is the ordered triple (dim U, dim V,dim U∩V ) of nonnegative integers. Assume that there are independent indeterminates corresponding to each type. Let Xq(n) be the Bq(n) × Bq(n) matrix whose entry in row U , column V is the indeterminate corresponding to the type of (U, V ). We factorize the determinant of Xq(n) into irreducible polynomials. |
| Starting Page | 17 |
| Ending Page | 29 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.13001/1081-3810.2892 |
| Volume Number | 29 |
| Alternate Webpage(s) | http://repository.uwyo.edu/cgi/viewcontent.cgi?article=2892&context=ela |
| Alternate Webpage(s) | http://repository.uwyo.edu/cgi/viewcontent.cgi?article=2892&context=ela&filename=1&type=additional |
| Alternate Webpage(s) | https://repository.uwyo.edu/cgi/viewcontent.cgi?article=2892&context=ela |
| Alternate Webpage(s) | https://doi.org/10.13001/1081-3810.2892 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
