Volume 18, issue 6 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 8, 3533–4008
Issue 7, 3059–3532
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The distribution of knots in the Petaluma model

Chaim Even-Zohar, Joel Hass, Nathan Linial and Tahl Nowik

Algebraic & Geometric Topology 18 (2018) 3647–3667
Bibliography
1 C Adams, O Capovilla-Searle, J Freeman, D Irvine, S Petti, D Vitek, A Weber, S Zhang, Bounds on übercrossing and petal numbers for knots, J. Knot Theory Ramifications 24 (2015) MR3334663
2 C Adams, T Crawford, B DeMeo, M Landry, A T Lin, M Montee, S Park, S Venkatesh, F Yhee, Knot projections with a single multi-crossing, J. Knot Theory Ramifications 24 (2015) MR3342136
3 C Adams, G Kehne, Bipyramid decompositions of multi-crossing link complements, preprint (2016) arXiv:1610.03830
4 H Brunn, Über verknotete kurven, from: "Verhandlungen des ersten internationalen Mathematiker-Kongresses" (editor F Rudio), Teubner (1897) 256
5 H Chapman, Asymptotic laws for random knot diagrams, J. Phys. A 50 (2017) MR3659108
6 S Chmutov, S Duzhin, J Mostovoy, Introduction to Vassiliev knot invariants, Cambridge Univ. Press (2012) MR2962302
7 P R Cromwell, Arc presentations of knots and links, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, P Traczyk, V G Turaev), Banach Center Publ. 42, Polish Acad. Sci. Inst. Math. (1998) 57 MR1634447
8 M Delbruck, Knotting problems in biology, (1961)
9 Y Diao, The knotting of equilateral polygons in 3, J. Knot Theory Ramifications 4 (1995) 189 MR1331746
10 Y Diao, N Pippenger, D W Sumners, On random knots, J. Knot Theory Ramifications 3 (1994) 419 MR1291869
11 N Dunfield, Random knots: a preliminary report, talk slides (2014)
12 P Erdös, On a lemma of Littlewood and Offord, Bull. Amer. Math. Soc. 51 (1945) 898 MR0014608
13 C Even-Zohar, Models of random knots, J. Appl. Comput. Topol. 1 (2017) 263
14 C Even-Zohar, The writhe of permutations and random framed knots, Random Structures Algorithms 51 (2017) 121 MR3668848
15 C Even-Zohar, J Hass, N Linial, T Nowik, Invariants of random knots and links, Discrete Comput. Geom. 56 (2016) 274 MR3530968
16 H L Frisch, E Wasserman, Chemical topology, J. Amer. Chem. Soc. 83 (1961) 3789
17 G Kehne, Bipyramid decompositions of multi-crossing link complements, Honors thesis, Williams College (2016)
18 M G Kreĭn, A A Nudel’man, The Markov moment problem and extremal problems, 417, Amer. Math. Soc. (1977) MR0458081
19 W B R Lickorish, An introduction to knot theory, 175, Springer (1997) MR1472978
20 K C Millett, Monte Carlo explorations of polygonal knot spaces, from: "Knots in Hellas ’98" (editors C Gordon, V F R Jones, L H Kauffman, S Lambropoulou, J H Przytycki), Ser. Knots Everything 24, World Sci. (2000) 306 MR1865714
21 N Pippenger, Knots in random walks, Discrete Appl. Math. 25 (1989) 273 MR1026336
22 S Ross, A first course in probability, Macmillan (1976) MR0380910
23 C E Soteros, D W Sumners, S G Whittington, Entanglement complexity of graphs in 3, Math. Proc. Cambridge Philos. Soc. 111 (1992) 75 MR1131480
24 D W Sumners, S G Whittington, Knots in self-avoiding walks, J. Phys. A 21 (1988) 1689 MR951053
25 D J A Welsh, On the number of knots and links, from: "Sets, graphs and numbers" (editors G Halász, L Lovász, D Miklós, T Szőnyi), Colloq. Math. Soc. János Bolyai 60, North-Holland (1992) 713 MR1218230