Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2002
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0209080 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911671202611200 |
|---|---|
| author | Snellman, Jan |
| author_facet | Snellman, Jan |
| contents | Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = \limsup_{n \to \infty} \sqrt[n]{a_n}, where a_n is the vector space dimension of the n'th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) \le \sqrt{a_2}. Using some results of Friedland on the maximal spectral radius of 0-1 matrices with a prescribed number of ones, we improve on this bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0209080 |
| institution | arXiv |
| publishDate | 2002 |
| record_format | arxiv |
| spellingShingle | Bounds for the Entropy of Graded Algebras Snellman, Jan Rings and Algebras 16W50, 05C50; 16P90, 05C20, 05C38 Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = \limsup_{n \to \infty} \sqrt[n]{a_n}, where a_n is the vector space dimension of the n'th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) \le \sqrt{a_2}. Using some results of Friedland on the maximal spectral radius of 0-1 matrices with a prescribed number of ones, we improve on this bound. |
| title | Bounds for the Entropy of Graded Algebras |
| topic | Rings and Algebras 16W50, 05C50; 16P90, 05C20, 05C38 |
| url | https://arxiv.org/abs/math/0209080 |