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pro vyhledávání: '"Dougherty, Michael P."'
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 the Catalan numbers. In this article, we introduce a large family of ne
Externí odkaz:
http://arxiv.org/abs/2306.08119
Autor:
Dougherty, Michael
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 this article, we connect this setting with the study of certain convex
Externí odkaz:
http://arxiv.org/abs/2201.11185
Autor:
Poch, Alexandra, Dougherty, Michael P., Roman, Robert A., Chorich, Lynn, Hawkins, Zoe, Kim, Soo-Hyun, Kim, Hyung-Goo, Layman, Lawrence C.
Publikováno v:
In Molecular and Cellular Endocrinology 1 August 2024 589
Autor:
Dougherty, Michael, McCammond, Jon
There are many different algebraic, geometric and combinatorial objects that one can attach to a complex polynomial with distinct roots. In this article we introduce a new object that encodes many of the existing objects that have previously appeared
Externí odkaz:
http://arxiv.org/abs/2104.07609
Publikováno v:
In F&S Science November 2023 4(4):286-293
Akademický článek
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Autor:
Dougherty, Michael, McCammond, Jon
Given any n-tuple of complex numbers, one can canonically define a polynomial of degree n+1 that has the entries of this n-tuple as its critical points. In 2002, Beardon, Carne, and Ng studied a map $\theta\colon \mathbb{C}^n\to \mathbb{C}^n$ which o
Externí odkaz:
http://arxiv.org/abs/1908.10477
Publikováno v:
Algebr. Geom. Topol. 20 (2020) 3505-3560
The n-strand braid group can be defined as the fundamental group of the configuration space of n unlabeled points in a closed disk based at a configuration where all n points lie in the boundary of the disk. Using this definition, the subset of braid
Externí odkaz:
http://arxiv.org/abs/1811.05603
Akademický článek
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Autor:
Dougherty, Michael, McCammond, Jon
There are two natural simplicial complexes associated to the noncrossing partition lattice: the order complex of the full lattice and the order complex of the lattice with its bounding elements removed. The latter is a complex that we call the noncro
Externí odkaz:
http://arxiv.org/abs/1707.06620