Zobrazeno 1 - 10
of 181
pro vyhledávání: '"Holm Thorsten"'
This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein and Retakh. It generalises several earlier results to this situation: A formula for frieze determinants, a $T$-path formula expressing the Laurent phenomenon, an
Externí odkaz:
http://arxiv.org/abs/2410.13507
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
Externí odkaz:
http://arxiv.org/abs/2403.09156
Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jorgense
Externí odkaz:
http://arxiv.org/abs/2306.12148
Autor:
Holm, Thorsten, Jorgensen, Peter
Frieze patterns have been introduced by Coxeter in the 1970's and have recently attracted renewed interest due to their close connection with Fomin-Zelevinsky's cluster algebras. Frieze patterns can be interpreted as assignments of values to the diag
Externí odkaz:
http://arxiv.org/abs/2212.11723
Publikováno v:
Open Mathematics, Vol 2, Iss 1, Pp 67-75 (2004)
Externí odkaz:
https://doaj.org/article/eb880077cc51406c8435d2d32130960f
The finite-dimensional symmetric algebras over an algebraically closed field, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, the weighted surface algebras a
Externí odkaz:
http://arxiv.org/abs/2006.13075
Autor:
Cuntz, Michael, Holm, Thorsten
Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values a
Externí odkaz:
http://arxiv.org/abs/2003.14208
Publikováno v:
Forum of Mathematics, Sigma 8 (2020) e17
Frieze patterns, as introduced by Coxeter in the 1970's, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpubli
Externí odkaz:
http://arxiv.org/abs/1909.02332
Publikováno v:
In Journal of Algebra 1 April 2023 619:822-859