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31 papers · 1 filter
Noncrossing Partition Lattices from Planar Configurations
Stella Cohen, Michael Dougherty, Andrew D. Harsh +1
The lattice of noncrossing partitions is well-known for its wide variety of combinatorial appearances and properties. For example, the lattice is rank-symmetric and enumerated by t…
The Polyhedral Tree Complex
Michael Dougherty
The tree complex is a simplicial complex defined in recent work of Belk, Lanier, Margalit, and Winarski with natural applications to mapping class groups and complex dynamics. In t…
Rooted Clusters for Graph LP Algebras
Esther Banaian, Sunita Chepuri, Elizabeth Kelley +1
LP algebras, introduced by Lam and Pylyavskyy, are a generalization of cluster algebras. These algebras are known to have the Laurent phenomenon, but positivity remains conjectural…
Demicaps in AG(4,3) and Their Relation to Maximal Cap Partitions
Jordan Awan, Clare Frechette, Yumi Li +1
In this paper, we introduce a fundamental substructure of maximal caps in the affine geometry that we call \emph{demicaps}. Demicaps provide a direct link to particular p…
H-chromatic symmetric functions
Nancy Mae Eagles, Angèle M. Foley, Alice Huang +2
We introduce -chromatic symmetric functions, , which use the -coloring of a graph to define a generalization of Stanley's chromatic symmetric functions. We say…
Matroids that classify forests
Lorenzo Traldi
Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.