Document Zbl 1358.05142 - zbMATH Open
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Realization of plucking polynomials. (English) Zbl 1358.05142
Summary: We give necessary and sufficient conditions for a given polynomial to be a plucking polynomial of a rooted tree. We discuss the fact that different rooted trees can have the same polynomial.
MSC:
| 05C31 | Graph polynomials |
| 05C05 | Trees |
| 58B34 | Noncommutative geometry (à la Connes) |
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
References:
| [1] | Dabkowski, M. K., Li, C. and Przytycki, J. H., Catalan states of lattice crossing, Topol. Appl.182 (2015) 1-15. · Zbl 1308.57010 |
| [2] | Kac, V. and Cheung, P., Quantum Calculus, (Springer, 2002). · Zbl 0986.05001 |
| [3] | Przytycki, J. H., Progress in distributive homology: From \(q\)-polynomial of rooted trees to Yang-Baxter homology, in Algebraic Structures in Low-Dimensional Topology, , Vol. 11 (European Mathematical Society, 2014), pp. 1449-1453. |
| [4] | J. H. Przytycki, \(q\)-polynomial invariant of rooted trees, Arnold Mathematical Journal, doi: 10.1007/S40598-016-0053-7; arXiv:1512.03080 [math.CO]. · Zbl 1358.05057 |
| [5] | Przytycki, J. H., Knots and graphs: Two centuries of interaction, in Knot Theory and Its Applications, Contemp. Math., Vol. 670 (2016), pp. 171-257. · Zbl 1357.57020 |
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