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- Greg Kuperberg
- 1996

Author(s): Kuperberg, Greg | Abstract: Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new… (More)

- Greg Kuperberg
- 1996

A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. It is also known as a spherical category, or a strict, monoidal… (More)

- Greg Kuperberg
- 2000

In a previous article [math.CO/9712207], we derived the alternating-sign matrix (ASM) theorem from the Izergin-Korepin determinant for a partition function for square ice with domain wall boundary.… (More)

We introduce a family of planar regions, called Aztec diamonds, and study the ways in which these regions can be tiled by dominoes. Our main result is a generating function that not only gives the… (More)

- Greg Kuperberg
- SIAM J. Comput.
- 2005

We present a quantum algorithm for the dihedral hidden subgroup problem (DHSP) with time and query complexity $2^{O(\sqrt{\log\ N})}$. In this problem an oracle computes a function $f$ on the… (More)

- Greg Kuperberg
- 1990

We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group $G$, the invariant counts homomorphisms from the… (More)

We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2n(n+1)/2 domino… (More)

- Greg Kuperberg
- 2003

Several authors have recently studied virtual knots and links because they admit invariants arising from R-matrices. We prove that every virtual link is uniquely represented by a link L SI in a… (More)

- Greg Kuperberg
- 2006

Abstract.We establish a version of the bottleneck conjecture, which in turn implies a partial solution to the Mahler conjecture on the product v(K) = (Vol K)(Vol K°) of the volume of a symmetric… (More)

We compare two natural bases for the invariant space of a tensor product of irreducible representations of A_2, or sl(3). One basis is the web basis, defined from a skein theory called the… (More)