.
"ActiveFedora::Aggregation::ListSource" .
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"en" .
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"The interlace polynomials introduced by Arratia, Bollobas and Sorkin extend to invariants of graphs with vertex weights, and these weighted interlace polynomials have several novel properties. One novel property is a version of the fundamental three-term formula\r\n\r\nq(G) = q(G - a) + q(G(ab) - b) + ((x - 1)(2) - 1)q(G(ab) - a - b)\r\n\r\nthat lacks the last term. It follows that interlace polynomial computations can be represented by binary trees rather than mixed binary-ternary trees. Binary computation trees provide a description of q(G) that is analogous to the activities description of the Tutte polynomial. If G is a tree or forest then these 'algorithmic activities' are associated with a certain kind of independent set in G. Three other novel properties are weighted pendant-twin reductions, which involve removing certain kinds of vertices from a graph and adjusting the weights of the remaining vertices in such a way that the interlace polynomials are unchanged. These reductions allow for smaller computation trees as they eliminate some branches. If a graph can be completely analysed using pendant-twin reductions, then its interlace polynomial can be calculated in polynomial time. An intuitively pleasing property is that graphs which can be constructed through graph substitutions have vertex-weighted interlace polynomials which can be obtained through algebraic substitutions." .
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"2010-01" .
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"Combinatorics, Probability and Computing" .
"Publication" .
"2011-01-06T14:44:42Z" .
"Traldi, L. 2010 \"Weighted interlace polynomials.\" Combinatorics, Probability and Computing 19 (1): 133-157." .
"2020-02-05T20:28:36.328246953+00:00"^^ .
"Natural Sciences" .
"Cambridge University Press" .
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"Mathematics" .
"noid:t148fh410" .
"hdl:10385/782" .
"http://rightsstatements.org/vocab/InC/1.0/" .
"Lafayette College" .
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"Weighted interlace polynomials"@en .
"Article" .
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"heidenwt@lafayette.edu" .
"2019-10-20T00:04:24.269089246+00:00"^^ .
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"Traldi, Lorenzo" .
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