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We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible neighbors are sampled from the existing vertices with probability proportional to degree. Of these possibilities, the new… (More)

- Christopher Hoffman, Matthew Kahle, Elliot Paquette
- Discrete & Computational Geometry
- 2017

A Poincaré-Hopf theorem in the spirit of Pugh is proven for compact orbifolds with boundary. The theorem relates the index sum of a smooth vector field in generic contact with the boundary orbifold to the EulerSatake characteristic of the orbifold and a boundary term. The boundary term is expressed as a sum of Euler characteristics of tangency and… (More)

- Tamás Keleti, Elliot Paquette
- The American Mathematical Monthly
- 2010

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