Noncommutative frieze patterns with coefficients
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911827268468736 |
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| author | Cuntz, Michael Holm, Thorsten Jorgensen, Peter |
| author_facet | Cuntz, Michael Holm, Thorsten Jorgensen, Peter |
| contents | Based on Berenstein and Retakh's notion of noncommutative polygons we introduce and study noncommutative frieze patterns. We generalize several notions and fundamental properties from the classic (commutative) frieze patterns to noncommutative frieze patterns, e.g. propagation formulae and $μ$-matrices, quiddity cycles and reduction formulae, and we show that local noncommutative exchange relations and local triangle relations imply all noncommutative exchange relations and triangle relations. Throughout, we allow coefficients, so we obtain generalizations of results from our earlier paper on frieze patterns with coefficients from the commutative to the noncommutative setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncommutative frieze patterns with coefficients Cuntz, Michael Holm, Thorsten Jorgensen, Peter Combinatorics 05E99, 13F60, 51M20 Based on Berenstein and Retakh's notion of noncommutative polygons we introduce and study noncommutative frieze patterns. We generalize several notions and fundamental properties from the classic (commutative) frieze patterns to noncommutative frieze patterns, e.g. propagation formulae and $μ$-matrices, quiddity cycles and reduction formulae, and we show that local noncommutative exchange relations and local triangle relations imply all noncommutative exchange relations and triangle relations. Throughout, we allow coefficients, so we obtain generalizations of results from our earlier paper on frieze patterns with coefficients from the commutative to the noncommutative setting. |
| title | Noncommutative frieze patterns with coefficients |
| topic | Combinatorics 05E99, 13F60, 51M20 |
| url | https://arxiv.org/abs/2403.09156 |