Polynomial Generalizations of Knot Colorings

التفاصيل البيبلوغرافية
العنوان:	Polynomial Generalizations of Knot Colorings
المؤلفون:	He, Rachael, Ho, Austin, Kalir, Dorian, Miller, Jacob, Zevenbergen, Matthew
المصدر:	The PUMP Journal of Undergraduate Research; Vol. 5 (2022): PUMP Journal of Undergraduate Research; 1-23 ; 2576-3725 ; 2765-8724
بيانات النشر:	Mathematics Department, California State University, Dominguez Hills
سنة النشر:	2022
المجموعة:	California State University (CSU): Open Journal Systems
مصطلحات موضوعية:	knot theory, knot invariants, Reidemeister moves
الوصف:	In the field of knot theory, knot invariants are properties preserved across all embeddings and projections of the same knot. Fox n-coloring is a classical knot invariant which associates to each knot projection a system of linear equations. We generalize Fox’s n-coloring by using two, not necessarily distinct, polynomials over a field F, which we say form a (g,f)F coloring. We introduce a sufficient condition, called strong, for a pair of polynomials to form a (g,f)F coloring. We confirm a family of pairs of linear polynomials each of which form a (g,f)F coloring. We prove that there are no strong pairs containing an irreducible quadratic polynomial over a field F not of characteristic two. Furthermore, we find a method to produce polynomials with unbounded degree that form colorings over suitable fields.
نوع الوثيقة:	article in journal/newspaper
وصف الملف:	application/pdf
اللغة:	English
Relation:	https://journals.calstate.edu/pump/article/view/2616/2376; https://journals.calstate.edu/pump/article/view/2616
DOI:	10.46787/pump.v5i0.2616
الاتاحة:	https://journals.calstate.edu/pump/article/view/2616 https://doi.org/10.46787/pump.v5i0.2616
Rights:	Copyright (c) 2022 Rachael He, Austin Ho, Dorian Kalir, Jacob Miller, Matthew Zevenbergen ; http://creativecommons.org/licenses/by-nc/4.0
رقم الانضمام:	edsbas.339A1EB8
قاعدة البيانات:	BASE

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الوصف
DOI:	10.46787/pump.v5i0.2616