Tangle machines
نویسندگان
چکیده
منابع مشابه
Tangle Machines
Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they share the same information content. The goal of tangle machine equivalence is to provide a context-independent method to select, from among many ways to perform a task, the ‘best’ way to perform the task. The...
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The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence classes of tangle machines, which are called invariants. This paper constructs invariants of tangle machines. Chief among these are the prime factorizations...
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In my thesis, I use the planar algebra defined by Bigelow [4] to describe the multivariate Alexander polynomial. The advantage to using a planar algebra in this way is that the multivariate Alexander polynomial generalizes to a multivariate tangle invariant up to Reidemeister I. The planar algebra that I used in my thesis is the Motzkin planar algebra, which has connections to the representatio...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2015
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2015.0111