Ground states and formal duality relations in the Gaussian core model (2009)
Cohn, Henry, Kumar, Abhinav, Schuermann, Achill
We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core...
Algorithmic design of self-assembling structures (2009)
We study inverse statistical mechanics: how can one design a potential function so as to produce a specified ground state? In this paper, we show that unexpectedly simple potential functions suffice...
Projective geometry over F1 and the Gaussian binomial coefficients (2009)
notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and algebra, but it is rarely discussed...
The Liar. The paradox of the liar, attributed to Epimenides, is best phrased in the form "This sentence is false. " That sentence cannot be true (since it claims to be untrue), and...
Point configurations that are asymmetric yet balanced (2008)
Cohn, Henry, Elkies, Noam D., Kumar, Abhinav, Schuermann, Achill
A configuration of particles confined to a sphere is balanced if they are in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance)....
Counterintuitive ground states in soft-core models (2008)
It is well known that statistical mechanics systems exhibit subtle behavior in high dimensions. In this paper, we show that certain natural soft-core models, such as the Gaussian core model, have...
Generating a Random Sink-Free Orientation (2007)
In Quadratic Time, Henry Cohn, Robin Pemantle
A sink-free orientation of a nite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to...
Generating a Random Sink-Free Orientation (2007)
In Quadratic Time, Henry Cohn, Robin Pemantle
A sink-free orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to...
Experimental study of energy-minimizing point configurations on spheres (2006)
Ballinger, Brandon, Blekherman, Grigoriy, Cohn, Henry, Giansiracusa, Noah, Kelly, Elizabeth, Schuermann, Achill
In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima...
Universally optimal distribution of points on spheres (2006)
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points)....
The D_4 root system is not universally optimal (2006)
Cohn, Henry, Conway, John H., Elkies, Noam D., Kumar, Abhinav
We prove that the D_4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal...
Uniqueness of the (22,891,1/4) spherical code (2006)
We use techniques of Bannai and Sloane to give a new proof that there is a unique (22,891,1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in...
A short proof of the simple continued fraction expansion of e (2006)
This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.
Experimental study of energy-minimizing point configurations on spheres (2006)
Brandon Ballinger, Grigoriy Blekherman, Henry Cohn
Abstract. In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new...
Group-theoretic algorithms for matrix multiplication (2005)
Cohn, Henry, Kleinberg, Robert, Szegedy, Balazs, Umans, Christopher
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard...
Group-theoretic algorithms for matrix multiplication (2005)
Henry Cohn, Robert Kleinberg, Balázs Szegedy, Christopher Umans
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard...
The densest lattice in twenty-four dimensions (2004)
In this research announcement we outline the methods used in our recent proof that the Leech lattice is the unique densest lattice in R^24. Complete details will appear elsewhere, but here we...
Projective geometry over F_1 and the Gaussian binomial coefficients (2004)
There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role...
Optimality and uniqueness of the Leech lattice among lattices (2004)
We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore...
Optimality and Uniqueness of the Leech Lattice Among Lattices (2004)
Abstract. We prove that the Leech lattice is the unique densest lattice in R 24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We...
A group-theoretic approach to fast matrix multiplication (2003)
Cohn, Henry, Umans, Christopher
We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of...
New upper bounds on sphere packings I (2003)
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds...
Generating A Random Sink-Free Orientation In (2002)
Quadratic Time Henry, Henry Cohn, Robin Pemantle, James Propp
A sink-free orientation of a nite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to...
New upper bounds on sphere packings I (2001)
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds...
New upper bounds on sphere packings II (2001)
We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related...
Generating a random sink-free orientation in quadratic time (2001)
Cohn, Henry, Pemantle, Robin, Propp, James
A sink-free orientation of a finite undirected graph is a choice of orientation for each edge such that every vertex has out-degree at least 1. Bubley and Dyer (1997) use Markov Chain Monte Carlo to...
Local statistics for random domino tilings of the Aztec diamond (2000)
Cohn, Henry, Elkies, Noam, Propp, James
We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will...
A variational principle for domino tilings (2000)
Cohn, Henry, Kenyon, Richard, Propp, James
We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical...
Symmetry and specializability in continued fractions (2000)
We study explicit continued fraction expansions for certain series. Some of these expansions have symmetry that generalizes some remarkable examples discovered independently by Kmosek and Shallit....
2-adic behavior of numbers of domino tilings (2000)
We study the 2-adic behavior of the number of domino tilings of a 2n-by-2n square as nvaries. It was previously known that this number was of the form 2^n f(n)^2, where f(n) is an odd, positive...
SYMMETRY AND SPECIALIZABILITY IN CONTINUED FRACTIONS (2000)
A number defined by a series does not in general have an interesting continued fraction expansion. There are, however, some exceptions, such as the series
2-Adic Behavior of Numbers of Domino Tilings (1999)
Henry Cohn, Parents Garnette Cohn, Lee Cohn
. We study the 2-adic behavior of the number of domino tilings of a 2n 2n square as n varies. It was previously known that this number was of the form 2 n f(n) 2 ,wheref(n) is an odd, positive...
2-Adic Behavior of Numbers of Domino Tilings (1999)
Henry Cohn, Parents Garnette Cohn, Lee Cohn
. We study the 2-adic behavior of the number of domino tilings of a 2n \Theta 2n square as n varies. It was previously known that this number was of the form 2 n f(n) 2 , where f(n) is an odd,...
The shape of a typical boxed plane partition (1998)
Cohn, Henry, Larsen, Michael, Propp, James
Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all...
A variational principle for domino tilings (1998)
Henry Cohn, Richard Kenyon, James Propp, Dedicated Pieter, Willem Kasteleyn
Abstract. We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a...
The Shape of a Typical Boxed Plane Partition (1998)
Henry Cohn, Michael Larsen, James Propp
. Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all...
A Variational Principle For Domino Tilings (1998)
Henry Cohn, Richard Kenyon, James Propp, Dedicated Pieter, Willem Kasteleyn
. We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical...
The shape of a typical boxed plane partition (1998)
Abstract. Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution...
The shape of a typical boxed plane partition (1998)
Abstract. Using a calculus of variations approach, we determine the shape of atypical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on...
A variational principle for domino tilings (1998)
Henry Cohn, Richard Kenyon, James Propp, Dedicated Pieter, Willem Kasteleyn
The effect of boundary conditions is, however, not entirely trivial and will be discussed in more detail in a subsequent paper. P. W. Kasteleyn, 1961 1.
Local Statistics For Random Domino Tilings Of The Aztec Diamond (1996)
Henry Cohn, Noam Elkies, James Propp
. We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond according to the uniform distribution on such tilings, the tiling will contain a...
The Shape Of A Typical Boxed Plane Partition (1996)
Henry Cohn, Michael Larsen, James Propp
. Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all...
Der "Gesetzesvorbehalt" in der preussischen Verfassungsurkunde. (1918)
Greifswald, R.- u. staatswiss. Diss., 1919 (Nur in beschränkter Anzahl für den Austausch).
Thesis (doctoral)--Albert-Ludwigs-Universität Freiburg im Breisgau, 1906.
"NO, NO, NO, NO!": Three Sons of Connecticut Who Opposed the Chinese Exclusion Acts
In 1882, with the passage of the initial Chinese Exclusion Act, the United States committed an overt act of discrimination against its resident Chinese population. The Act, signed by then President...
Algorithmic design of self-assembling structures
We study inverse statistical mechanics: how can one design a potential function so as to produce a specified ground state? In this article, we show that unexpectedly simple potential functions...
POINT CONFIGURATIONS THAT ARE ASYMMETRIC YET BALANCED
Henry Cohn, Noam D. Elkies, Abhinav Kumar, Sch Ürmann
Abstract. A configuration of particles confined to a sphere is balanced if they are in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of...