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Dylan Heuer, Ph.D. - Milwaukee School of Engineering. Milwaukee, WI, US

Dylan Heuer, Ph.D. Dylan Heuer, Ph.D.

Instructor | Milwaukee School of Engineering

Milwaukee, WI, UNITED STATES

Dr. Dylan Heuer's research area is in combinatorics and deals with various generalizations of permutations and alternating sign matrices.

Education, Licensure and Certification (3)

Ph.D.: Mathematics, North Dakota State University 2021

M.S.: Mathematics, North Dakota State University 2018

B.A.: Mathematics and Music, Concordia College 2013

Biography

Dr. Dylan Heuer is an instructor for the Mathematics Department at Milwaukee School of Engineering. In 2021, he completed his Ph.D. in mathematics at North Dakota State University. Heuer's research area is in combinatorics and deals with various generalizations of permutations and alternating sign matrices. Learning and using Sagemath has been an integral part of his research. Heuer loves teaching mathematics, and has had the opportunity to teach a wide variety of courses ranging from Intermediate Algebra to Calculus to upper-level Combinatorics.

Areas of Expertise (3)

Mathematics

Combinatorics

Sagemath

Accomplishments (1)

NDSU Mathematics Department Graduate Student Teaching Award (professional)

2019

Event and Speaking Appearances (1)

Partial Permutohedra

Algebra & Discrete Mathematics Seminar  North Dakota State University

2021-03-23

Selected Publications (2)

Partial permutation and alternating sign matrix polytopes

arXiv:2012.09901

We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial permutohedra that we show arise naturally as projections of these polytopes. We enumerate facets and also characterize the face lattices of partial permutohedra in terms of chains in the Boolean lattice.

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Chained permutations and alternating sign matrices—Inspired by three-person chess

Discrete Mathematics

We define and enumerate two new two-parameter permutation families, namely, placements of a maximum number of non-attacking rooks on chained-together chessboards, in either a circular or linear configuration. The linear case with corresponds to standard permutations of , and the circular case with and corresponds to a three-person chessboard.

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