Alternating sign matrices and domino tilings
- N. Elkies, G. Kuperberg, M. Larsen, J. Propp
- Mathematics
- 1 June 1991
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…
Motivic measures and stable birational geometry
We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the…
Finite subgroups of algebraic groups
Generalizing a classical theorem of Jordan to arbitrary characteristic,
we prove that every finite subgroup of GLn
over a field of any characteristic
p possesses a subgroup of bounded index which…
The Shape of a Typical Boxed Plane Partition
- Henry Cohn, M. Larsen, J. Propp
- Mathematics
- 13 January 1998
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…
Grothendieck ring of pretriangulated categories
We consider the abelian group PT generated by quasi-equivalence classes of pretriangulated DG categories with relations coming from semiorthogonal decompositions of corresponding triangulated…
A Modular Functor Which is Universal¶for Quantum Computation
- M. Freedman, M. Larsen, Zhenghan Wang
- Physics
- 29 January 2000
Abstract:We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently…
Alternating-Sign Matrices and Domino Tilings (Part I)
- N. Elkies, G. Kuperberg, M. Larsen, J. Propp
- Mathematics
- 2 September 1992
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…
Topological Quantum Computation
- M. Freedman, A. Kitaev, M. Larsen, Zhenghan Wang
- Physics
- 4 January 2001
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly-…
Alternating-Sign Matrices and Domino Tilings (Part II)
- N. Elkies, G. Kuperberg, M. Larsen, J. Propp
- Mathematics
- 2 November 1992
We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main…
Determining representations from invariant dimensions
This paper is motivated by the following "Tannakian" question: to what extent is a complex Lie group, G, and a finite dimensional representation, (p, V) of G, determined by the dimensions of the…
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