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It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describing the effect of taking a signed tensor… (More)

- Yuanan Diao, Gábor Hetyei, Kenneth Hinson
- Graphs and Combinatorics
- 2009

We show how the results of Brylawski and Oxley [4] on the Tutte polynomial of a tensor product of graphs may be generalized to colored graphs and the Tutte polynomials introduced by Bollobás and Riordan [1]. This is a generalization of our earlier work on signed graphs with applications to knot theory. Our result makes the calculation of certain invariants… (More)

- Yuanan Diao, Gábor Hetyei, Kenneth Hinson
- Eur. J. Comb.
- 2011

We provide a new proof of Brylawski's formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte's formula, expressing the Tutte polynomial using a calculus of activities, to all polynomials involved in Brylawski's formula. The approach presented here may be used to show a signed generalization of Brylawski's… (More)

- Kenneth E. Hinson, Marvin G. Cline, +5 authors Kesha Evette Hinson
- 2002

(Abstract) Research on the comparison of educational aspirations among Black and White students has produced conflicting results. Some studies at the national level have shown that the level of educational aspirations for college between these two groups is similar, while other studies at the state, regional, or local level have shown differences. The… (More)

Surveying the results of three recent papers and some currently ongoing research, we show how a generalization of Brylawski's tensor product formula to colored graphs may be used to compute the Jones polynomial of some fairly complicated knots and, in the future, even virtual knots. Résumé. En faisant une revue de trois articles récents et de la recherche… (More)

It is well-known that the Jones polynomial of a knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. In this paper, we study the Tutte polynomials for signed graphs. We show that if a signed graph is constructed from a simpler graph via k-thickening or k-stretching, then its Tutte polynomial can… (More)

- J. Arsuaga, T. Blackstone, Y. Diao, K. Hinson, E. Karadayi, M. Saito
- 2007

DNA knots formed under extreme conditions of condensation, as in bacteriophage P4, are difficult to analyze experimentally and theoretically. In this paper, we propose to use the uniform random polygon model as a supplementary method to the existing methods for generating random knots in confinement. The uniform random polygon model allows us to sample… (More)

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