P. Tumarkin

collaborators

5 papers

math.CO2026

Growth of infinite frieze patterns of affine type

Karin Baur, Anna Felikson, Deepanshu Prasad +2

We analyse the growth coefficients of infinite frieze patterns arising from cluster algebras using cluster modular groups and cluster categories. For a fixed cluster category of af…

math.CO2026

$S L_{2}$ -tilings with translational symmetry

Veronique Bazier-Matte, Marie-Anne Bourgie, Anna Felikson +1

An $S L_{2}$ -tiling is a bi-infinite matrix in which all adjacent $2 \times 2$ minors are equal to $1$ . Positive integral $S L_{2}$ -tilings were introduced by Assem, Reutenauer and Smith…

math.CO2025

Friezes from surfaces and Farey triangulation

Anna Felikson, Pavel Tumarkin

We provide a classification of positive integral friezes on marked bordered surfaces in the style of Conway and Coxeter. More precisely, we prove that positive integral friezes are…

math.CO2025

Punctured surfaces, quiver mutations, and quotients of Coxeter groups

Anna Felikson, Michael Shapiro, Pavel Tumarkin

In 2011, Barot and Marsh provided an explicit construction of presentation of a finite Weyl group $W$ by any quiver mutation-equivalent to an orientation of a Dynkin diagram with W…

math.RT2025

Categorifications of Non-Integer Quivers: Type $I_{2} (2 n)$

Drew Damien Duffield, Pavel Tumarkin

We use weighted unfoldings of quivers to provide a categorification of mutations of quivers of types $I_{2} (2 n)$ , thus extending the construction of categorifications of mutations of…