@article{chandler_sazdanovic_stella_yip_2023, title={On the strength of chromatic symmetric homology for graphs}, volume={150}, ISSN={["1090-2074"]}, url={http://dx.doi.org/10.1016/j.aam.2023.102559}, DOI={10.1016/j.aam.2023.102559}, abstractNote={In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for graphs to a homological setting, and its Frobenius characteristic is a q,t generalization of the chromatic symmetric function. We exhibit three pairs of graphs where each pair has the same chromatic symmetric function but distinct homology over C as Sn-modules. We also show that integral chromatic symmetric homology contains torsion, and based on computations, conjecture that Z2-torsion in bigrading (1,0) detects nonplanarity in the graph.}, journal={ADVANCES IN APPLIED MATHEMATICS}, author={Chandler, Alex and Sazdanovic, Radmila and Stella, Salvatore and Yip, Martha}, year={2023}, month={Sep} } @article{nakanishi_stella_2016, title={WONDER OF SINE-GORDON Y-SYSTEMS}, volume={368}, ISSN={["1088-6850"]}, DOI={10.1090/tran/6505}, abstractNote={The sine-Gordon Y-systems and the reduced sine-Gordon Y-systems were introduced by Tateo in the 90's in the study of the integrable deformation of conformal field theory by the thermodynamic Bethe ansatz method. The periodicity property and the dilogarithm identities concerning these Y-systems were conjectured by Tateo, and only a part of them have been proved so far. In this paper we formulate these Y-systems by the polygon realization of cluster algebras of types A and D, and prove the conjectured periodicity and dilogarithm identities in full generality. As it turns out, there is a wonderful interplay among continued fractions, triangulations of polygons, cluster algebras, and Y-systems.}, number={10}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Nakanishi, Tomoki and Stella, Salvatore}, year={2016}, month={Oct}, pages={6835–6886} } @article{nakanishi_stella_2014, title={Diagrammatic description of c-vectors and d-vectors of cluster algebras of finite type}, volume={21}, number={1}, journal={Electronic Journal of Combinatorics}, author={Nakanishi, T. and Stella, S.}, year={2014} }