On the HOMFLY polynomials of even trigonal bipyramid links

Even trigonal bipyramid links ( ETB links ) are the mathematical models of DNA trigonal bipyramids such that each edge is composed of a twist tangle with 2 n -crossing number (Lin et al. in J Mol Graph Model 95: 107492, 2020). In this paper, a basis of ETB links has been introduced as a set of trivi...

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Published in:	Journal of mathematical chemistry Vol. 60; no. 3; pp. 542 - 554
Main Authors:	Lin, Haoyu, Zhang, Heng, Liu, Shuya
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.03.2022 Springer Nature B.V
Subjects:	Algorithms Chemistry Chemistry and Materials Science Links Math. Applications in Chemistry Mathematical models Original Paper Physical Chemistry Polynomials Predictive control Programming languages Theoretical and Computational Chemistry HOMFLY polynomial Python program Topological chirality Polyhedral links DNA trigonal bipyramid
ISSN:	0259-9791, 1572-8897
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Abstract	Even trigonal bipyramid links ( ETB links ) are the mathematical models of DNA trigonal bipyramids such that each edge is composed of a twist tangle with 2 n -crossing number (Lin et al. in J Mol Graph Model 95: 107492, 2020). In this paper, a basis of ETB links has been introduced as a set of trivial links obtained from any ETB link by respectively smoothing and switching each crossing, which is used to calculate the HOMFLY polynomial of each ETB link. Hence through establishing the algorithm for computing the HOMFLY polynomials of ETB links, an ETBL program has been developed in the Python programming language. As a result, the HOMFLY polynomials of 104 families of ETB links are given in terms of the parameter n . Based on these polynomials, we show that all ETB links are all chiral. Also, the structural property of 30 pairs of link families is further explored due to each pair of links having the same HOMFLY polynomial. These results provide a necessary theoretical support for predicting and controlling the topological structures of DNA trigonal bipyramids.
AbstractList	Even trigonal bipyramid links ( ETB links ) are the mathematical models of DNA trigonal bipyramids such that each edge is composed of a twist tangle with 2 n -crossing number (Lin et al. in J Mol Graph Model 95: 107492, 2020). In this paper, a basis of ETB links has been introduced as a set of trivial links obtained from any ETB link by respectively smoothing and switching each crossing, which is used to calculate the HOMFLY polynomial of each ETB link. Hence through establishing the algorithm for computing the HOMFLY polynomials of ETB links, an ETBL program has been developed in the Python programming language. As a result, the HOMFLY polynomials of 104 families of ETB links are given in terms of the parameter n . Based on these polynomials, we show that all ETB links are all chiral. Also, the structural property of 30 pairs of link families is further explored due to each pair of links having the same HOMFLY polynomial. These results provide a necessary theoretical support for predicting and controlling the topological structures of DNA trigonal bipyramids. Even trigonal bipyramid links (ETB links) are the mathematical models of DNA trigonal bipyramids such that each edge is composed of a twist tangle with 2n-crossing number (Lin et al. in J Mol Graph Model 95: 107492, 2020). In this paper, a basis of ETB links has been introduced as a set of trivial links obtained from any ETB link by respectively smoothing and switching each crossing, which is used to calculate the HOMFLY polynomial of each ETB link. Hence through establishing the algorithm for computing the HOMFLY polynomials of ETB links, an ETBL program has been developed in the Python programming language. As a result, the HOMFLY polynomials of 104 families of ETB links are given in terms of the parameter n. Based on these polynomials, we show that all ETB links are all chiral. Also, the structural property of 30 pairs of link families is further explored due to each pair of links having the same HOMFLY polynomial. These results provide a necessary theoretical support for predicting and controlling the topological structures of DNA trigonal bipyramids.
Author	Liu, Shuya Zhang, Heng Lin, Haoyu
Author_xml	– sequence: 1 givenname: Haoyu surname: Lin fullname: Lin, Haoyu organization: Key Laboratory of Colloid and Interface Chemistry, Ministry of Education, Shandong University, College of Chemistry and Molecular Engineering, Peking University – sequence: 2 givenname: Heng surname: Zhang fullname: Zhang, Heng organization: Key Laboratory of Colloid and Interface Chemistry, Ministry of Education, Shandong University – sequence: 3 givenname: Shuya surname: Liu fullname: Liu, Shuya email: liushuya@sdu.edu.cn organization: Key Laboratory of Colloid and Interface Chemistry, Ministry of Education, Shandong University
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Snippet	Even trigonal bipyramid links ( ETB links ) are the mathematical models of DNA trigonal bipyramids such that each edge is composed of a twist tangle with 2 n... Even trigonal bipyramid links (ETB links) are the mathematical models of DNA trigonal bipyramids such that each edge is composed of a twist tangle with...
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Title	On the HOMFLY polynomials of even trigonal bipyramid links
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