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- Faculty Publications (281)
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- 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
- July 2012
- Article
Discrete Choice Cannot Generate Demand That Is Additively Separable in Own Price
By: Sonia Jaffe and Scott Duke Kominers
We show that in a unit demand discrete choice framework with at least three goods, demand cannot be additively separable in own price. This result sharpens the analogous result of Jaffe and Weyl (2010) in the case of linear demand and has implications for testing of... View Details
- Article
On the Correspondence of Contracts to Salaries in (Many-to-Many) Matching
In this note, I extend the work of Echenique (2012) to show that a model of many-to-many matching with contracts may be embedded into a model of many-to-many matching with wage bargaining whenever (1) all agentsʼ preferences are substitutable and (2) the matching with... View Details
- Article
Testing Substitutability
By: John William Hatfield, Nicole Immorlica and Scott Duke Kominers
We provide an algorithm for testing the substitutability of a length-N preference relation over a set of contracts X in time O(|X|3⋅N3). Access to the preference relation is essential for this result: We show that a substitutability-testing algorithm with access only... View Details
- Article
Holdout in the Assembly of Complements: A Problem for Market Design
By: Scott Duke Kominers and E. Glen Weyl
Holdout problems prevent private (voluntary and self-financing) assembly of complementary goods—such as land or dispersed spectrum—from many self-interested sellers. While mechanisms that fully respect sellers' property rights cannot alleviate these holdout problems,... View Details
- Article
Matching in Networks with Bilateral Contracts
By: John William Hatfield and Scott Duke Kominers
We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (many-to-many) matching with contracts, as well as supply chain matching. When firms' relationships do not... View Details
- 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
- Article
Stability and Competitive Equilibrium in Matching Markets with Transfers
By: John William Hatfield and Scott Duke Kominers
This note surveys recent work in generalized matching theory, focusing on trading networks with transferable utility. In trading networks with a finite set of contractual opportunities, the substitutability of agents’ preferences is essential for the guaranteed... View Details
Keywords: Matching; Networks; Joint Ventures; Stability; Competitive Equilibrium; Core; Efficiency; Economics; Theory
- November 2011
- Teaching Note
Duke Energy and the Nuclear Renaissance (TN)
Keywords: Energy Generation
- October 2011
- Supplement
Online Marketing at Big Skinny — slide supplement
By: Benjamin Edelman and Scott Duke Kominers
Slide Supplement for 911-034 View Details
Keywords: Consumer Products Industry
- September 2011 (Revised February 2014)
- Case
Duke Energy and the Nuclear Renaissance
Duke Energy, an American investor-owned electric utility, confronts multibillion dollar decisions about its future fuel mix. In particular, its leaders are considering building new nuclear capacity. Whether this is sensible depends, among other things, on demand... View Details
- 2011
- Book
Success with Science: The Winners' Guide to High School Research
By: Shiv Gaglani, Maria Elena De Obaldia, Scott Duke Kominers, Dayan Li and Carol Y. Suh
Do you want to develop useful skills, gain admission to top colleges, win scholarship money, excel at science competitions, and explore career options all while having fun? By reading this book and using the advice within it, you will learn how to formulate a research... View Details
- February 2011 (Revised February 2012)
- Case
Online Marketing at Big Skinny
By: Benjamin Edelman and Scott Duke Kominers
Describes a wallet maker's application of seven Internet marketing technologies: display ads, algorithmic search, sponsored search, social media, interactive content, online distributors, and A/B testing. Provides concise introductions to the key features of each... View Details
- Article
Every Large Point Set Contains Many Collinear Points or an Empty Pentagon
By: Zachary Abel, Brad Ballinger, Prosenjit Bose, Sébastien Collette, Vida Dujmović, Ferran Hurtado, Scott Duke Kominers, Stefan Langerman, Attila Pór and David Wood
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique”... View Details
- 2010
- Working Paper
Agglomerative Forces and Cluster Shapes
By: William R. Kerr and Scott Duke Kominers
We model spatial clusters of similar firms. Our model highlights how agglomerative forces lead to localized, individual connections among firms, while interaction costs generate a defined distance over which attraction forces operate. Overlapping firm interactions... View Details
- Article
A Constant Bound for the Periods of Parallel Chip-firing Games with Many Chips
By: Paul Myer Kominers and Scott Duke Kominers
We prove that any parallel chip-firing game on a graph G with at least 4|E(G)| − |V(G)| chips stabilizes, i.e., such a game has eventual period of length 1. Furthermore, we obtain a polynomial bound on the number of rounds before stabilization. This result is a... View Details
- 2010
- Article
A Categorical Construction of Ultrafilters
By: Daniel Litt, Zachary Abel and Scott Duke Kominers
- 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