1,820 research outputs found
A determinant formula for the Jones polynomial of pretzel knots
This paper presents an algorithm to construct a weighted adjacency matrix of
a plane bipartite graph obtained from a pretzel knot diagram. The determinant
of this matrix after evaluation is shown to be the Jones polynomial of the
pretzel knot by way of perfect matchings (or dimers) of this graph. The weights
are Tutte's activity letters that arise because the Jones polynomial is a
specialization of the signed version of the Tutte polynomial. The relationship
is formalized between the familiar spanning tree setting for the Tait graph and
the perfect matchings of the plane bipartite graph above. Evaluations of these
activity words are related to the chain complex for the Champanerkar-Kofman
spanning tree model of reduced Khovanov homology.Comment: 19 pages, 12 figures, 2 table
Improving the fairness of FAST TCP to new flows
It has been observed that FAST TCP, and the related protocol TCP Vegas, suffer unfairness when many flows arrive at a single bottleneck link, without intervening departures. We show that the effect is even more marked if a new flow arrives when existing flows share bandwidth fairly, and propose a simple method to ameliorate this effect
Sizes of Minimum Connected Dominating Sets of a Class of Wireless Sensor Networks
We consider an important performance measure of wireless sensor networks, namely, the least number of nodes, N, required to facilitate routing between any pair of nodes, allowing other nodes to remain in sleep mode in order to conserve energy. We derive the expected value and the distribution of N for single dimensional dense networks
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