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- Faculty Publications (271)
Duke →
- 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...
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Keywords:
Entrepreneurship;
Geographic Location;
Patents;
Labor;
Industry Clusters;
Industry Structures;
Relationships;
Competitive Advantage;
Technology Industry;
California
Kerr, William R., and Scott Duke Kominers. "Agglomerative Forces and Cluster Shapes." Harvard Business School Working Paper, No. 11-061, December 2010.
- 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...
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Kominers, Paul Myer, and Scott Duke Kominers. "A Constant Bound for the Periods of Parallel Chip-firing Games with Many Chips." Archiv der Mathematik 95, no. 1 (July 2010): 9–13.
- Article
Course Allocation by Proxy Auction
By: Scott Duke Kominers, Mike Ruberry and Jonathan Ullman
Kominers, Scott Duke, Mike Ruberry, and Jonathan Ullman. "Course Allocation by Proxy Auction." Proceedings of the International Workshop on Internet and Network Economics 6th (2010): 551–558. (Lecture Notes in Computer Science, Vol. 6484.)
- 2010
- Article
A Categorical Construction of Ultrafilters
By: Daniel Litt, Zachary Abel and Scott Duke Kominers
Litt, Daniel, Zachary Abel, and Scott Duke Kominers. "A Categorical Construction of Ultrafilters." Rocky Mountain Journal of Mathematics 40, no. 5 (2010): 1611–1617.
- 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 >=...
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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.
- March 2010
- Article
Matching with Preferences over Colleagues Solves Classical Matching
In this note, we demonstrate that the problem of "many-to-one matching with (strict) preferences over colleagues" is actually more difficult than the classical many-to-one matching problem, "matching without preferences over colleagues." We give an explicit reduction...
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Kominers, Scott Duke. "Matching with Preferences over Colleagues Solves Classical Matching." Games and Economic Behavior 68, no. 2 (March 2010): 773–780.
- 2010
- Article
On Congruence Conditions for Primality
By: Sherry Gong and Scott Duke Kominers
Gong, Sherry, and Scott Duke Kominers. "On Congruence Conditions for Primality." A26. INTEGERS: Electronic Journal of Combinatorial Number Theory 10 (2010): 313–317.
- Article
Shape Replication Through Self-Assembly and RNase Enzymes
By: Zachary Abel, Nadia Benbernou, Mirela Damian, Erik D. Demaine, Robin Flatland, Scott Duke Kominers, Robert Schweller and Martin L. Demaine
Abel, Zachary, Nadia Benbernou, Mirela Damian, Erik D. Demaine, Robin Flatland, Scott Duke Kominers, Robert Schweller, and Martin L. Demaine. "Shape Replication Through Self-Assembly and RNase Enzymes." Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms 21st (2010): 1045–1064.
- 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...
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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
Information Can Wreck Cooperation: A Counterpoint to Kandori (1992)
By: Yuichiro Kamada and Scott Duke Kominers
Kamada, Yuichiro, and Scott Duke Kominers. "Information Can Wreck Cooperation: A Counterpoint to Kandori (1992)." Economics Letters 107, no. 2 (May 2010): 112–114.
- Article
Irrational Roots Revisited
Kominers, Scott Duke. "Irrational Roots Revisited." Mathematical Gazette 94, no. 530 (July 2010): 303–304.
- 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...
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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).
- Article
Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80
By: Noam D. Elkies and Scott Duke Kominers
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms...
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Keywords:
Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80." Proceedings of the American Mathematical Society 138, no. 1 (January 2010): 105–108.
- September 2009
- Article
Finding Matrices that Satisfy Functional Equations
Kominers, Scott Duke. "Finding Matrices that Satisfy Functional Equations." College Mathematics Journal 40, no. 4 (September 2009): 289–292. (As part of "Classroom Capsules.")
- June 2009
- Article
How Concepts Affect Consumption
By: Dan Ariely and Michael I. Norton
Duke behavioral economist Ariely and Harvard Business School professor Norton explore how our consumption of concepts influences physical consumption, both positively and negatively.
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Ariely, Dan, and Michael I. Norton. "How Concepts Affect Consumption." Harvard Business Review 87, no. 6 (June 2009).
- 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.
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Keywords:
Mathematical Methods
Kominers, Scott Duke. "Configurations of Extremal Even Unimodular Lattices." International Journal of Number Theory 5, no. 3 (May 2009): 457–464.
- Response
A Correspondence Note on Myerson's 'Irrationality via Well-ordering'
Kominers, Scott Duke. "A Correspondence Note on Myerson's 'Irrationality via Well-ordering'." Gazette of the Australian Mathematical Society 36, no. 1 (March 2009): 53.
- 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.
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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.
- Article
Leonard Bernstein's Doodles: Reading Outside the Lines at the Library of Congress
Kominers, Scott Duke. "Leonard Bernstein's Doodles: Reading Outside the Lines at the Library of Congress." Special Issue on Leonard Bernstein in Boston. Journal of the Society for American Music 3, no. 1 (February 2009): 26–33. (As an appendix to "Leonard Bernstein's Jewish Boston: Cross-Disciplinary Research in the Classroom" by Carol J. Oja and Kay Kaufman Shelemay.)
- 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...
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Keywords:
Mathematical Methods
Kominers, Scott Duke. "On Universal Binary Hermitian Forms." A02. INTEGERS: Electronic Journal of Combinatorial Number Theory 9 (2009): 9–15.