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Show Results For
- All HBS Web
(839)
- News (77)
- Research (639)
- Events (12)
- Multimedia (4)
- Faculty Publications (635)
- Article
Hinged Dissections Exist
By: Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine and Scott Duke Kominers
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form... View Details
Abbott, Timothy G., Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott Duke Kominers. "Hinged Dissections Exist." Discrete & Computational Geometry 47, no. 1 (January 2012): 150–186.
- 2009
- Article
On Universal Binary Hermitian Forms
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
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
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
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
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
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
- March 2004
- Teaching Note
Variance Analysis Tutorial (Instructor Guide)
By: David F. Hawkins
Instructor Guide to (9-104-709). View Details
Keywords: Mathematical Methods
- 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
Maister, David H. "Note on the Management of Queues." Harvard Business School Background Note 680-053, October 1979. (Revised March 1995.)
- 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
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.
- July 2023
- Article
Design and Analysis of Switchback Experiments
By: Iavor I Bojinov, David Simchi-Levi and Jinglong Zhao
In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted... View Details
Bojinov, Iavor I., David Simchi-Levi, and Jinglong Zhao. "Design and Analysis of Switchback Experiments." Management Science 69, no. 7 (July 2023): 3759–3777.
- January 1997
- Background Note
Simulation as a Decision Aid
By: Roy D. Shapiro
A brief introduction to simulation--what it is, why it's used, etc. Meant to set context for a first class on simulation. A rewritten version of an earlier note. View Details
Shapiro, Roy D. "Simulation as a Decision Aid." Harvard Business School Background Note 697-062, January 1997.
- Career Coach
Wendi Zhang
development policies and analysis in the public sector. Wendi attended the Massachusetts Institute of Technology, where she received Bachelor of Science degrees in both Mathematics and Management Science, along with minors in Economics... View Details
- 1969
- Other Unpublished Work
An Empirical Investigation of the Samuelson Rational Warrant Pricing Theory
By: Robert C. Merton
- 01 Mar 2023
- News
The Latest Model
understanding of network effects, revenue models, and ecosystem development. Given its founders’ academic pedigrees—Barrera studied with Nobel laureate Oliver Hart; Hurder with Nobel laureate and HBS professor emeritus Al Roth—Prysm also is more View Details
- Oct 2020
- Conference Presentation
Optimal, Truthful, and Private Securities Lending
By: Emily Diana, Michael J. Kearns, Seth Neel and Aaron Leon Roth
We consider a fundamental dynamic allocation problem motivated by the problem of securities lending in financial markets, the mechanism underlying the short selling of stocks. A lender would like to distribute a finite number of identical copies of some scarce resource... View Details
Diana, Emily, Michael J. Kearns, Seth Neel, and Aaron Leon Roth. "Optimal, Truthful, and Private Securities Lending." Paper presented at the 1st Association for Computing Machinery (ACM) International Conference on AI in Finance (ICAIF), October 2020.
- 2013
- Working Paper
Applying Random Coefficient Models to Strategy Research: Testing for Firm Heterogeneity, Predicting Firm-Specific Coefficients, and Estimating Strategy Trade-Offs
By: Juan Alcacer, Wilbur Chung, Ashton Hawk and Goncalo Pacheco-de-Almeida
Although Strategy research aims to understand how firm actions have differential effects on performance, most empirical research estimates the average effects of these actions across firms. This paper promotes Random Coefficients Models (RCMs) as an ideal empirical... View Details
Alcacer, Juan, Wilbur Chung, Ashton Hawk, and Goncalo Pacheco-de-Almeida. "Applying Random Coefficient Models to Strategy Research: Testing for Firm Heterogeneity, Predicting Firm-Specific Coefficients, and Estimating Strategy Trade-Offs." Harvard Business School Working Paper, No. 14-022, September 2013.
- Article
Consistent Covariance Matrix Estimation with Cross-Sectional Dependence and Heteroskedasticity in Cross-Sectional Financial Data
By: K. A. Froot
Keywords: Econometrics; Panel Estimation; Autocorrelation; Heteroskedasticity; Mathematical Methods; Economics
Froot, K. A. "Consistent Covariance Matrix Estimation with Cross-Sectional Dependence and Heteroskedasticity in Cross-Sectional Financial Data." Journal of Financial and Quantitative Analysis 24, no. 3 (September 1989): 333–355. (Revised from NBER Technical Working Paper No. 62.)