71,058 research outputs found
A permanent formula for the Jones polynomial
The permanent of a square matrix is defined in a way similar to the
determinant, but without using signs. The exact computation of the permanent is
hard, but there are Monte-Carlo algorithms that can estimate general
permanents. Given a planar diagram of a link L with crossings, we define a
7n by 7n matrix whose permanent equals to the Jones polynomial of L. This
result accompanied with recent work of Freedman, Kitaev, Larson and Wang
provides a Monte-Carlo algorithm to any decision problem belonging to the class
BQP, i.e. such that it can be computed with bounded error in polynomial time
using quantum resources.Comment: To appear in Advances in Applied Mathematic
Bounds on the number of connected components for tropical prevarieties
For a tropical prevariety in Rn given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of connected components is less than k+7n−
Transitive Triangle Tilings in Oriented Graphs
In this paper, we prove an analogue of Corr\'adi and Hajnal's classical
theorem. There exists such that for every when the following holds. If is an oriented graph on vertices and every
vertex has both indegree and outdegree at least , then contains a
perfect transitive triangle tiling, which is a collection of vertex-disjoint
transitive triangles covering every vertex of . This result is best
possible, as, for every , there exists an oriented graph
on vertices without a perfect transitive triangle tiling in which every
vertex has both indegree and outdegree at least Comment: To appear in Journal of Combinatorial Theory, Series B (JCTB
Direct Interactions in Relativistic Statistical Mechanics
Directly interacting particles are considered in the multitime formalism of
predictive relativistic mechanics. When the equations of motion leave a
phase-space volume invariant, it turns out that the phase average of any first
integral, covariantly defined as a flux across a -dimensional surface, is
conserved. The Hamiltonian case is discussed, a class of simple models is
exhibited, and a tentative definition of equilibrium is proposed.Comment: Plain Tex file, 26 page
On -core and self-conjugate -core partitions in arithmetic progressions
We extend recent results of Ono and Raji, relating the number of
self-conjugate -core partitions to Hurwitz class numbers. Furthermore, we
give a combinatorial explanation for the curious equality
. We also conjecture
that an equality of this shape holds if and only if , proving the cases
and giving partial results for
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