R-systems by Galashin, Pavel, Pylyavskyy, Pavlo

“…We show that in many cases, singularity confinement in an R-system reduces to the Laurent phenomenon either in a cluster algebra, or in a Laurent phenomenon algebra, or beyond both of those generalities, giving rise to many new sequences with the Laurent property possessing rich groups of symmetries. …”
Get full text

Weak Separation, Pure Domains and Cluster Distance by Farber, Miriam, Galashin, Pavel

“…We apply our result to calculate the cluster distance and to give lower bounds on the mutation distance between cluster variables in the cluster algebra structure on the coordinate ring of the Grassmannian. …”
Get full text

Non-perturbative geometries for planar N $$ \mathcal{N} $$ = 4 SYM... by Arkani-Hamed, Nima, Lam, Thomas, Spradlin, Marcus

“…Abstract There is a remarkable well-known connection between the G(4, n) cluster algebra and n-particle amplitudes in N $$ \mathcal{N} $$ = 4 SYM theory. …”
Get full text

Arrangements of equal minors in the positive Grassmannian by Farber, Miriam, Postnikov, Alexander

“…Weakly separated sets, originally introduced by Leclerc and Zelevinsky, are closely related to the positive Grassmannian and the associated cluster algebra. However, we also construct examples of arrangements of smallest minors which are not weakly separated using chain reactions of mutations of plabic graphs. …”
Get full text
Get full text
Get full text

A cluster of results on amplituhedron tiles by Even-Zohar, Chaim, Lakrec, Tsviqa, Parisi, Matteo, Sherman-Bennett, Melissa, Tessler, Ran, Williams, Lauren

“…It generalizes cyclic polytopes and the positive Grassmannian and has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the 𝑚=4 amplituhedron. …”
Get full text

POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS by POSTNIKOV, ALEXANDER

“…Remarkably, the same combinatorial structures appeared in many other areas of mathematics and physics, e.g., in the study of cluster algebras, scattering amplitudes, and solitons. …”
Get full text

Sortable Elements for Quivers with Cycles by Reading, Nathan, Speyer, David E.

“…The c-sortable elements are closely tied to the combinatorics of cluster algebras with an acyclic seed; the ultimate motivation behind this paper is to extend this connection beyond the acyclic case.…”
Get full text

Stringy canonical forms by Arkani-Hamed, Nima, He, Song, Lam, Thomas

“…We also discuss a number of other examples, including stringy canonical forms for finite-type cluster algebras (with type A corresponding to usual string amplitudes), and other natural integrals over the positive Grassmannian.…”
Get full text