2016/08/19 by Meena Jagadeesan, Jagadeesan, Meena
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.1608.05723
openalex publication_date 2016/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Weakly separated collections arise in the cluster algebra derived from the Plücker coordinates on the nonnegative Grassmannian. Oh, Postnikov, and Speyer studied weakly separated collections over a general Grassmann necklace I and proved the connectivity of every exchange graph. Oh and Speyer later introduced a generalization of exchange graphs that we call C-constant graphs. They characterized these graphs in the smallest two cases. We prove an isomorphism between exchange graphs and a certain class of C-constant graphs. We use this to extend Oh and Speyer's characterization of these graphs to the smallest four cases, and we present a conjecture on a bound on the maximal order of these graphs. In addition, we fully characterize certain classes of these graphs in the special cases of cycles and trees.