Publications

November 2004 (Revised April 2005)
Background Note

Math for Strategists

By: Tarun Khanna and Jan W. Rivkin

Great strategists rely heavily on numbers as they go about their work. Offers an overview of the high- and low-brow quantitative tools that students encounter during the Strategy course. The class explores high-brow tools in detail; the focus here is on low-brow... View Details

Keywords: Mathematical Methods; Strategy

Educators

Purchase

fall 1973
Article

Statistical Sampling in Auditing with Auxiliary Information Estimators

By: Robert S. Kaplan

Keywords: Mathematical Methods; Information

2022
Working Paper

A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure

By: Jesse M. Shapiro and Liyang Sun

Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in... View Details

Keywords: Econometric Models; Mathematical Methods

March 2022
Article

Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models

By: Fiammetta Menchetti and Iavor Bojinov

Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details

Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods

2021
Working Paper

Population Interference in Panel Experiments

By: Iavor I Bojinov, Kevin Wu Han and Guillaume Basse

The phenomenon of population interference, where a treatment assigned to one experimental unit affects another experimental unit's outcome, has received considerable attention in standard randomized experiments. The complications produced by population interference in... View Details

Keywords: Finite Population; Potential Outcomes; Dynamic Causal Effects; Mathematical Methods

SSRN

September 2021
Article

Oh's 8-Universality Criterion Is Unique

By: Scott Duke Kominers

Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh’s 8-universality criterion as an... View Details

Keywords: N-universal Lattice; 8-universal Lattice; Universality Criteria; Quadratic Forms; Additively Indecomposable; Mathematical Methods

2021
Article

Prisoners, Rooms, and Lightswitches

By: Daniel M. Kane and Scott Duke Kominers

We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his n prisoners in and out of r rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The... View Details

Keywords: Mathematical Methods

2019
Article

Configurations of Extremal Type II Codes via Harmonic Weight Enumerators

By: Noam D. Elkies and Scott Duke Kominers

We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details

Keywords: Mathematical Methods

2019
Article

Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading

By: Iavor I Bojinov and Neil Shephard

We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of a broad class of these estimands and exact randomization based p-values for testing causal... View Details

Keywords: Causality; Nonparametric; Potential Outcomes; Trading Costs; Mathematical Methods

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Article

A New Proof of Serre's Homological Characterization of Regular Local Rings

By: Ravi Jagadeesan and Aaron Landesman

We give a new proof of Serre’s result that a Noetherian local ring is regular if and only if it has finite global dimension. Our proof avoids the explicit construction of a Koszul complex. View Details

Keywords: Mathematical Methods

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

Purchase

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

2018
Working Paper

Semi-Parametric Estimation of Dynamic Discrete Choice Models

By: David Hao Zhang

I develop a new method for estimating counterfactuals in dynamic discrete choice models, a widely used set of models in economics, without requiring a distributional assumption on utility shocks. Applying my method to the canonical Rust (1987) setting, I find that the... View Details

Keywords: Semiparametrics; Dynamic Discrete Choice; Consumer Choice; Mathematical Methods

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

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

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