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Show Results For
- All HBS Web
(1,918)
- People (2)
- News (215)
- Research (1,370)
- Events (15)
- Multimedia (13)
- Faculty Publications (906)
- Article
Improved Bounds on the Sizes of S.P Numbers
By: Paul Myer Kominers and Scott Duke Kominers
A number which is S.P in base r is a positive integer which is equal to the sum of its base-r digits multiplied by the product of its base-r digits. These numbers have been studied extensively in The Mathematical Gazette. Recently, Shah Ali... View Details
Keywords: Mathematical Methods
Kominers, Paul Myer, and Scott Duke Kominers. "Improved Bounds on the Sizes of S.P Numbers." Mathematical Gazette 94, no. 529 (March 2010): 127–129.
- Article
Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)
By: Scott Duke Kominers and Zachary Abel
We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1. View Details
Keywords: Mathematical Methods
Kominers, Scott Duke, and Zachary Abel. "Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)." Journal de Théorie des Nombres de Bordeaux 20, no. 2 (2008): 365–371.
- August 2005 (Revised April 2008)
- Teaching Note
Store24 (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
- fall 1992
- Article
Exploring the Limits of the Technology S-curve, Part 1: Component Technologies
By: Clayton M. Christensen
Christensen, Clayton M. "Exploring the Limits of the Technology S-curve, Part 1: Component Technologies." Production and Operations Management 1 (fall 1992): 334–357.
- 20 Mar 2001 - 21 Mar 2001
- Conference Presentation
QAP: The Quadratic Assignment Procedure
By: William B. Simpson
Keywords: Mathematical Methods
Simpson, William B. "QAP: The Quadratic Assignment Procedure." Paper presented at the North American Stata Users' Group Meeting, March 20–21, 2001.
- 1979
- Dissertation
Inference in Partially Identified Models
By: Dutch Leonard
Keywords: Mathematical Methods
- 1982
- Chapter
Informal Covariation Assessment: Data-based vs. Theory-based Judgements
By: D. Jennings, T. M. Amabile and L. D. Ross
Keywords: Mathematical Methods
- November 1993
- Article
Stable Matchings, Optimal Assignments, and Linear Programming
By: A. E. Roth, U. G. Rothblum and J. H. Vande Vate
Keywords: Mathematical Methods
Roth, A. E., U. G. Rothblum, and J. H. Vande Vate. "Stable Matchings, Optimal Assignments, and Linear Programming." Mathematics of Operations Research 18, no. 4 (November 1993): 803–828.
- 2013
- Article
Beyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux
By: Nihal Gowravaram and Ravi Jagadeesan
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West’s notion of shape-Wilf equivalence to apply to alternating... View Details
Keywords: Pattern Avoidance; Alternating Permutations; Descent Type Permutations; Wilf Equivalence; Shape-Wilf Equivalence; Mathematical Methods
Gowravaram, Nihal, and Ravi Jagadeesan. "Beyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux." #P17. Electronic Journal of Combinatorics 20, no. 4 (2013).
- 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.
- 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.
- 19 Oct 2017
- Working Paper Summaries
Games of Threats
- 22 Oct 2020
- Working Paper Summaries
Estimating Causal Effects in the Presence of Partial Interference Using Multivariate Bayesian Structural Time Series Models
Keywords: by Fiammetta Menchetti and Iavor Bojinov