Alternation by region crossing changes and implications for warping span-Reference-Cited by-同舟云学术

Alternation by region crossing changes and implications for warping span

Published:2016-11 Issue:13 Volume:25 Page:1650073
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Kreinbihl James¹,Martin Ra’jene²,Murphy Colin³,Renn McKenna⁴,Townsend Jennifer⁵^ORCID

Affiliation:

1. Wesleyan University, USA, 45 Wyllys Ave, Middletown, CT 06459, United States

2. Duke University, USA, Durham, NC 27708, United States

3. Seattle University, USA, 901 12th Ave, Seattle, WA 98122, United States

4. University of Washington, USA, Seattle, WA, United States

5. Faculty of Mathematics, Bellevue College, 3000 Landerholm Circle SE, Bellevue WA 98007, United States

Abstract

We examine the number of region crossing changes necessary to produce alternation of a diagram. This property leads to an invariant similar to the dealternating number, but which offers new insight. In particular, we apply the reasoning built for this invariant to prove that (warping) span of any knot is at most 2.

Funder

National Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216516500735

Reference6 articles.

1. THE DEALTERNATING NUMBER AND THE ALTERNATION NUMBER OF A CLOSED 3-BRAID

2. Almost alternating links

3. A polynomial invariant of virtual knots

4. CROSSING INFORMATION AND WARPING POLYNOMIALS ABOUT THE TREFOIL KNOT

5. Alternating distances of knots and links

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