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  • All HBS Web  (857)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)

Show Results For

  • All HBS Web  (857)
    • News  (79)
    • Research  (640)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)
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  • 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.
  • 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
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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
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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
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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
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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
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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
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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
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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
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"Variance Analysis Tutorial." Harvard Business School Tutorial 104-709, March 2004.
  • March 2004
  • Tutorial

HBS Quantitative Analysis Course

By: Janice H. Hammond
Keywords: Mathematical Methods
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"HBS Quantitative Analysis Course." Harvard Business School Tutorial 604-702, March 2004.
  • 1977
  • Article

On the Joint Distribution of Left- and Right-sided Outliner Statistics

By: André Perold and D. M. Hawkins
Keywords: Mathematical Methods
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Perold, André, and D. M. Hawkins. "On the Joint Distribution of Left- and Right-sided Outliner Statistics." Utilitas mathematica 12 (1977): 129–143.
  • Article

Eliminating Unintended Bias in Personalized Policies Using Bias-Eliminating Adapted Trees (BEAT)

By: Eva Ascarza and Ayelet Israeli

An inherent risk of algorithmic personalization is disproportionate targeting of individuals from certain groups (or demographic characteristics such as gender or race), even when the decision maker does not intend to discriminate based on those “protected”... View Details

Keywords: Algorithm Bias; Personalization; Targeting; Generalized Random Forests (GRF); Discrimination; Customization and Personalization; Decision Making; Fairness; Mathematical Methods
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Ascarza, Eva, and Ayelet Israeli. "Eliminating Unintended Bias in Personalized Policies Using Bias-Eliminating Adapted Trees (BEAT)." e2115126119. Proceedings of the National Academy of Sciences 119, no. 11 (March 8, 2022).
  • January 2006
  • Tutorial

Cost-Volume Profit Models

By: David F. Hawkins, V.G. Narayanan, Jacob Cohen and Michele Jurgens
Covers fixed, variable, and semivariable costs and their role in building and interpreting cost-volume-profit models. Introduces the cost-volume and contribution-volume-profit models and identifies some of their uses and limitations. Teaches how to use the... View Details
Keywords: Volume; Cost; Profit; Mathematical Methods
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"Cost-Volume Profit Models." Harvard Business School Tutorial 105-705, January 2006.
  • 2007
  • Working Paper

Mental Accounting and Small Windfalls: Evidence from an Online Grocer

By: Katherine L. Milkman, John Beshears, Todd Rogers and Max H. Bazerman
We study the effect of small windfalls on consumer spending decisions by examining the purchasing behavior of a sample of online grocery shoppers over the course of a year. We compare the purchases customers make when redeeming a $10-off coupon they received from their... View Details
Keywords: Spending; Consumer Behavior; Mathematical Methods; Food and Beverage Industry; Retail Industry
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Milkman, Katherine L., John Beshears, Todd Rogers, and Max H. Bazerman. "Mental Accounting and Small Windfalls: Evidence from an Online Grocer." Harvard Business School Working Paper, No. 08-024, September 2007. (Revised March 2008.)
  • 18 Sep 2019
  • Working Paper Summaries

Using Models to Persuade

Keywords: by Joshua Schwartzstein and Adi Sunderam
  • September 1993 (Revised August 2011)
  • Exercise

ExtendSim® Simulation Exercises in Process Analysis (A)

By: Roy D. Shapiro
First set of exercises meant to be used with ExtendSim, a simulation system created by Imagine That, Inc. of San Jose, California. These exercises allow students to investigate the impact of variable processing times on the performance of simple in-line processes.... View Details
Keywords: Operations; Business Processes; Performance; Mathematical Methods
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Shapiro, Roy D. "ExtendSim® Simulation Exercises in Process Analysis (A)." Harvard Business School Exercise 694-039, September 1993. (Revised August 2011.)
  • 1 Dec 1998
  • Conference Presentation

An Introduction to Mixed Models in SAS

By: William B. Simpson
Keywords: Applications and Software; Mathematical Methods
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Simpson, William B. "An Introduction to Mixed Models in SAS." Boston Area SAS Users Group, Boston, MA, December 1, 1998.
  • 2024
  • Working Paper

Fiscal Policy under Convex Supply Curves

By: Shlok Goyal, Avi Lipton and Borui Niklas Zhu
Recent empirical evidence suggests that supply curves are convex. Supply curve convexity is at odds with conventional Phillips curves, which rely on an infinitely elastic underlying supply curve. This paper explores the effect of supply curve convexity on the... View Details
Keywords: Fiscal Stimulus; Fiscal Policy; Inflation; Inflation and Deflation; Macroeconomics; Policy; Mathematical Methods; United States
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Goyal, Shlok, Avi Lipton, and Borui Niklas Zhu. "Fiscal Policy under Convex Supply Curves." Working Paper, August 2024.
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