Report
On cogrowth function of algebras and its logarithmical gap
| العنوان: | On cogrowth function of algebras and its logarithmical gap |
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| المؤلفون: | Kanel-Belov, A. J., Melnikov, I. A., Mitrofanov, I. V. |
| المصدر: | Comptes Rendus - S\'erie Mathe\'ematique., 359:3 (2021), 297-303 |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, Mathematics - Combinatorics, 16S15, 37B10 |
| الوصف: | Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal $I$-reducible word. A {\em cogrowth} function is number of obstructions of length $\le n$. We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth. Comment: 5 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.5802/crmath.170 |
| URL الوصول: | http://arxiv.org/abs/1912.03345 |
| رقم الانضمام: | edsarx.1912.03345 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.5802/crmath.170 |
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