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- Faculty Publications (568)
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- All HBS Web (618)
- Faculty Publications (568)
- 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
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
Jagadeesan, Ravi. "Ascent-Descent Young Diagrams and Pattern Avoidance in Alternating Permutations." #P3.9. Electronic Journal of Combinatorics 21, no. 3 (2014).
- 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
Alcacer, Juan, and Minyuan Zhao. "Zooming In: A Practical Manual for Identifying Geographic Clusters." Strategic Management Journal 37, no. 1 (January 2016): 10–21.
- 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
Elkies, Noam D., and Scott Duke Kominers. "Weighted Generating Functions for Type II Lattices and Codes." In Quadratic and Higher Degree Forms. Vol. 31, edited by Alladi Krishnaswami, Manjul Bhargava, David Savitt, and Pham Huu Tiep, 63–108. Developments in Mathematics. Springer, 2013.
- 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
Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
- 1987
- Chapter
Continuous-Time Stochastic Models
By: Robert C. Merton
Keywords: Mathematical Methods
Merton, Robert C. "Continuous-Time Stochastic Models." In The New Palgrave: A Dictionary of Economic Theory and Doctrine, edited by John Eatwell, Murray Milgate, and Peter Newman. London: Macmillan Press, 1987. (Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd., 1992.)
- February 1996
- Exercise
Problems in Variance Analysis
By: William J. Bruns Jr.
Keywords: Mathematical Methods
Bruns, William J., Jr. "Problems in Variance Analysis." Harvard Business School Exercise 196-120, February 1996.
- May 1983
- Article
Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming
By: André Perold and R. Meidan
Keywords: Mathematical Methods
Perold, André, and R. Meidan. "Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming." Journal of Optimization Theory and Applications 40, no. 1 (May 1983): 61–76.
- February 2005 (Revised November 2006)
- Background Note
Using Data Desk for Statistical Analysis
By: Frances X. Frei and Dennis Campbell
Describes how to use the Data Desk software package to perform statistical analysis. View Details
Keywords: Mathematical Methods
Frei, Frances X., and Dennis Campbell. "Using Data Desk for Statistical Analysis." Harvard Business School Background Note 605-060, February 2005. (Revised November 2006.)
- March 2004
- Tutorial
Variance Analysis Tutorial
By: David F. Hawkins and Jacob Cohen
An interactive tutorial on variance analysis, flexible budgets, and overhead allocation. View Details
Keywords: Mathematical Methods
- 1977
- Article
On the Joint Distribution of Left- and Right-sided Outliner Statistics
By: André Perold and D. M. Hawkins
Keywords: Mathematical Methods
Perold, André, and D. M. Hawkins. "On the Joint Distribution of Left- and Right-sided Outliner Statistics." Utilitas mathematica 12 (1977): 129–143.
- 1972
- Chapter
Random Walks and Technical Theories: Some Additional Evidence
By: George A. Benington and Michael C. Jensen
Keywords: Mathematical Methods
Benington, George A., and Michael C. Jensen. "Random Walks and Technical Theories: Some Additional Evidence." In Security Evaluation and Portfolio Analysis, edited by E. Elton and M. Gruber. Prentice Hall, 1972. (Also published in Journal of Finance (May 1970) and Investment Management: Some Readings, J. Lorie and R. Brealey, Editors (Praeger Publishers, 1972).)
- 1979
- Article
An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem
By: C. Blair and A. E. Roth
Keywords: Mathematical Methods
Blair, C., and A. E. Roth. "An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem." Algebra Universalis 9 (1979): 131–132.
- January 1975
- Article
A Lattice Fixed-Point Theorem with Constraints
By: A. E. Roth
Keywords: Mathematical Methods
Roth, A. E. "A Lattice Fixed-Point Theorem with Constraints." Bulletin of the American Mathematical Society 81 (January 1975): 136–138.
- 2018
- Working Paper
Bundling Incentives in (Many-to-Many) Matching with Contracts
By: Jonathan Ma and Scott Duke Kominers
In many-to-many matching with contracts, the way in which contracts are specified can affect the set of stable equilibrium outcomes. Consequently, agents may be incentivized to modify the set of contracts upfront. We consider one simple way in which agents may do so:... View Details
Keywords: Matching With Contracts; Contract Design; Bundling-proofness; Substitutability; Mathematical Methods
Ma, Jonathan, and Scott Duke Kominers. "Bundling Incentives in (Many-to-Many) Matching with Contracts." Harvard Business School Working Paper, No. 19-011, August 2018.
- 2011
- Chapter
Fundamental Data Anomalies
By: Ian D. Gow
Gow, Ian D. "Fundamental Data Anomalies." Chap. 5 in The Handbook of Equity Market Anomalies: Translating Market Inefficiencies into Effective Investment Strategies, edited by Len Zacks, 117–128. John Wiley & Sons, 2011.
- November 1990 (Revised November 1992)
- Background Note
Note on Linear Programming
Gives an elementary introduction to formulating linear programming models and interpreting linear programmings output. Other aspects of linear programming are discussed briefly. View Details
Keywords: Mathematical Methods
Eckstein, Jonathan. "Note on Linear Programming." Harvard Business School Background Note 191-085, November 1990. (Revised November 1992.)
- August 2005 (Revised April 2008)
- Teaching Note
GuestFirst Hotel (A): 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
- 2001
- Other Teaching and Training Material
Interaction Terms in Regression
By: William B. Simpson and Kimball Lewis
Keywords: Mathematical Methods
Simpson, William B., and Kimball Lewis. "Interaction Terms in Regression." 2001. Electronic.