Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Felikson, Anna"'
Autor:
Felikson, Anna, Tumarkin, Pavel
We provide a classification of positive integral friezes on marked bordered surfaces. The classification is similar to the Conway--Coxeter's one: positive integral friezes are in one-to-one correspondence with ideal triangulations supplied with a col
Externí odkaz:
http://arxiv.org/abs/2410.13511
We explore a three-dimensional counterpart of the Farey tessellation and its relations to Penner's lambda lengths and $SL_2$-tilings. In particular, we prove a three-dimensional version of Ptolemy relation, and generalise results of Ian Short to clas
Externí odkaz:
http://arxiv.org/abs/2306.17118
Autor:
Felikson, Anna
In recent decades, identities similar to the one in the Ptolemy's theorem started to pop up in many fields in connection to the notion of cluster algebras introduced and studied since 2000 by Fomin and Zelevinsky. In this brief note we will try to de
Externí odkaz:
http://arxiv.org/abs/2302.06379
Frieze patterns are numerical arrangements that satisfy a local arithmetic rule. These arrangements are actively studied in connection to the theory of cluster algebras. In the setting of cluster algebras, the notion of a frieze pattern can be genera
Externí odkaz:
http://arxiv.org/abs/2111.13135
Autor:
Felikson, Anna, Tumarkin, Pavel
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
Comment: v3: a mistake concerning $X_6$ quiver is corrected (Theorem 6.2). 39 pages, many figures
Comment: v3: a mistake concerning $X_6$ quiver is corrected (Theorem 6.2). 39 pages, many figures
Externí odkaz:
http://arxiv.org/abs/2110.12917
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with every triangu
Externí odkaz:
http://arxiv.org/abs/2008.00480
Autor:
Felikson, Anna, Lampe, Philipp
Skew-symmetric non-integer matrices with real entries can be viewed as quivers with non-integer weights of arrows. One can mutate such quivers according to usual rules of quiver mutation. Felikson and Tumarkin show that rank 3 mutation-finite non-int
Externí odkaz:
http://arxiv.org/abs/1904.03928
Autor:
Felikson, Anna, Tumarkin, Pavel
We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrizable matrix has a geometric realization by reflections. We also explore the structure of acyclic represe
Externí odkaz:
http://arxiv.org/abs/1902.01997
Autor:
Felikson, Anna, Lampe, Philipp
Publikováno v:
In Journal of Geometry and Physics June 2023 188
Autor:
Felikson, Anna, Tumarkin, Pavel
Publikováno v:
Adv. Math. 340 (2018), 855--882
We establish a bijective correspondence between certain non-self-intersecting curves in an $n$-punctured disc and positive ${\mathbf c}$-vectors of acyclic cluster algebras whose quivers have multiple arrows between every pair of vertices. As a corol
Externí odkaz:
http://arxiv.org/abs/1709.10360