Methods - Publications - Faculty & Research

October 2015
Article

A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants

By: Ravi Jagadeesan

We study the action of Gal(ℚ^⎯/ℚ) on the category of Belyĭ functions (finite étale covers of ℙ^1_(ℚ^⎯) \ {0,1,∞}. We describe a new combinatorial Gal(ℚ^⎯/ℚ)‐invariant for Belyĭ functions whose monodromy cycle types above 0 and ∞ are the same. We use a version of our... View Details

Keywords: Mathematical Methods

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2014
Article

Ascent-Descent Young Diagrams and Pattern Avoidance in Alternating Permutations

By: Ravi Jagadeesan

We investigate pattern avoidance in alternating permutations and an alternating analogue of Young diagrams. In particular, using an extension of Babson and West’s notion of shape-Wilf equivalence described in our recent paper (with N. Gowravaram), we generalize results... View Details

Keywords: Pattern Avoidance; Alternating Permutations; Shape-Wilf Equivalence; Mathematical Methods

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January 2016
Article

Zooming In: A Practical Manual for Identifying Geographic Clusters

By: Juan Alcacer and Minyuan Zhao

This paper takes a close look at the reasons, procedures, and results of cluster identification methods. Despite being a popular research topic in strategy, economics, and sociology, geographic clusters are often studied with little consideration given to the... View Details

Keywords: Mathematical Methods

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2013
Chapter

Weighted Generating Functions for Type II Lattices and Codes

By: Noam D. Elkies and Scott Duke Kominers

We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we... View Details

Keywords: Mathematical Methods

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Article

Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions

By: Daniel M. Kane and Scott Duke Kominers

For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained... View Details

Keywords: Mathematical Methods

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