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Publications

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  • All HBS Web  (837)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)

Show Results For

  • All HBS Web  (837)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
← Page 12 of 837 Results →
  • 2009
  • Article

On Universal Binary Hermitian Forms

By: Scott Duke Kominers
Earnest and Khosravani, Iwabuchi, and Kim and Park recently gave a complete classification of the universal binary Hermitian forms. We give a unified proof of the universalities of these Hermitian forms, relying upon Ramanujan's list of universal quadratic forms... View Details
Keywords: Mathematical Methods
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Kominers, Scott Duke. "On Universal Binary Hermitian Forms." A02. INTEGERS: Electronic Journal of Combinatorial Number Theory 9 (2009): 9–15.
  • May 2009
  • Article

Configurations of Extremal Even Unimodular Lattices

By: Scott Duke Kominers
We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. View Details
Keywords: Mathematical Methods
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Kominers, Scott Duke. "Configurations of Extremal Even Unimodular Lattices." International Journal of Number Theory 5, no. 3 (May 2009): 457–464.
  • 2010
  • Article

On the Classification of Type II Codes of Length 24

By: Noam D. Elkies and Scott Duke Kominers
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of the root systems of Type II... View Details
Keywords: Mathematical Methods
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Elkies, Noam D., and Scott Duke Kominers. "On the Classification of Type II Codes of Length 24." SIAM Journal on Discrete Mathematics 23, no. 4 (2010).
  • March 2010
  • Article

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

By: Shaofang Hong and Scott Duke Kominers
For relatively prime positive integers u_0 and r, we consider the arithmetic progression {u_k := u_0+k*r} (0 <= k <= n). Define L_n := lcm{u_0,u_1,...,u_n} and let a >= 2 be any integer. In this paper, we show that, for integers alpha,r >= a and n >=... View Details
Keywords: Mathematical Methods
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Hong, Shaofang, and Scott Duke Kominers. "Further Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Proceedings of the American Mathematical Society 138, no. 3 (March 2010): 809–813.
  • August 2005 (Revised April 2008)
  • Teaching Note

GuestFirst Hotel (B): Statistics Review with Data Desk (TN)

By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
Keywords: Mathematical Methods; Accommodations Industry
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Frei, Frances X. "GuestFirst Hotel (B): Statistics Review with Data Desk (TN)." Harvard Business School Teaching Note 606-039, August 2005. (Revised April 2008.)
  • March 2004
  • Teaching Note

Variance Analysis Tutorial (Instructor Guide)

By: David F. Hawkins
Instructor Guide to (9-104-709). View Details
Keywords: Mathematical Methods
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Hawkins, David F. "Variance Analysis Tutorial (Instructor Guide)." Harvard Business School Teaching Note 104-077, March 2004.
  • October 1979 (Revised March 1995)
  • Background Note

Note on the Management of Queues

Contains four sections: 1) measuring the performance of queuing systems; 2) types of queuing systems; 3) the behavior of simple systems (elementary queuing theory); and 4) the management of queues (including a discussion of their psychology). View Details
Keywords: Mathematical Methods
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Maister, David H. "Note on the Management of Queues." Harvard Business School Background Note 680-053, October 1979. (Revised March 1995.)
  • 1994
  • Chapter

Industry Analysis

By: D. J. Collis and P. Ghemawat
Keywords: Mathematical Methods
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Collis, D. J., and P. Ghemawat. "Industry Analysis." In The Portable MBA in Strategy, edited by Liam Fahey and Robert M. Randall. New York: John Wiley & Sons, 1994.
  • 1997
  • Chapter

On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios

By: Robert C. Merton
Keywords: Mathematical Methods
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Merton, Robert C. "On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios." In The Legacy of Norbert Wiener: A Centennial Symposium. Vol. 60, edited by D. Jerison, I. M. Singer, and D. W. Stroock. Proceedings of Symposia in Pure Mathematics . Providence, RI: American Mathematical Society, 1997.
  • 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
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Shapiro, Jesse M., and Liyang Sun. "A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure." NBER Working Paper Series, No. 29976, April 2022.
  • 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
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Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
  • 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
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Bojinov, Iavor I., Kevin Wu Han, and Guillaume Basse. "Population Interference in Panel Experiments." Harvard Business School Working Paper, No. 21-100, March 2021.
  • 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
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Kominers, Scott Duke. "Oh's 8-Universality Criterion Is Unique." Kyungpook Mathematical Journal 61, no. 3 (September 2021): 455–459.
  • 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
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Kane, Daniel M., and Scott Duke Kominers. "Prisoners, Rooms, and Lightswitches." Electronic Journal of Combinatorics 28, no. 1 (2021).
  • 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
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Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes via Harmonic Weight Enumerators." Journal de Théorie des Nombres de Bordeaux 31, no. 3 (2019): 679–688.
  • 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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Bojinov, Iavor I., and Neil Shephard. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading." Journal of the American Statistical Association 114, no. 528 (2019): 1665–1682.
  • 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
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Jagadeesan, Ravi, and Aaron Landesman. "A New Proof of Serre's Homological Characterization of Regular Local Rings." Art. 18. Research in Number Theory 2 (December 2016).
  • 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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Jagadeesan, Ravi. "A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants." Proceedings of the London Mathematical Society 111, no. 4 (October 2015): 911–935.
  • 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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Jagadeesan, Ravi. "Ascent-Descent Young Diagrams and Pattern Avoidance in Alternating Permutations." #P3.9. Electronic Journal of Combinatorics 21, no. 3 (2014).
  • 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
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Zhang, David Hao. "Semi-Parametric Estimation of Dynamic Discrete Choice Models." Working Paper, April 2018.
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