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Author ID: ernst.claus Recent zbMATH articles by "Ernst, Claus"
Published as: Ernst, C.; Ernst, Claus
Homepage: https://www.wku.edu/math/facultystaff/claus_ernst
External Links: MGP · ORCID · dblp
Documents Indexed: 61 Publications since 1987, including 1 Additional arXiv Preprint
Reviewing Activity: 203 Reviews
Co-Authors: 28 Co-Authors with 54 Joint Publications
404 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

54 Publications have been cited 368 times in 187 Documents Cited by Year
A calculus for rational tangles: Applications to DNA recombination. Zbl 0727.57005
Ernst, C.; Sumners, D. W.
50
1990
The growth of the number of prime knots. Zbl 0632.57007
Ernst, C.; Sumners, D. W.
33
1987
Thickness of knots. Zbl 0924.57010
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
22
1999
The complexity of lattice knots. Zbl 0924.57007
Diao, Y.; Ernst, C.
19
1998
Solving tangle equations arising in a DNA recombination model. Zbl 0916.57013
Ernst, C.; Sumners, D. W.
18
1999
Tangle equations. Zbl 0857.57005
Ernst, C.
14
1996
Knot energies by ropes. Zbl 0889.57005
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
11
1997
The linear growth in the lengths of a family of thick knots. Zbl 1046.57006
Diao, Y.; Ernst, C.; Thistlethwaite, M.
11
2003
Hamiltonian knot projections and lengths of thick knots. Zbl 1040.57004
Diao, Yuanan; Ernst, Claus; Yu, Xingxing
11
2004
Nullification of knots and links. Zbl 1241.57005
Diao, Yuanan; Ernst, Claus; Montemayor, Anthony
10
2012
\(N\)-string tangles. Zbl 1001.57009
Emert, J.; Ernst, C.
10
2000
Generating equilateral random polygons in confinement. II. Zbl 1320.60033
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
9
2012
Upper bounds on linking numbers of thick lines. Zbl 0998.57013
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
9
2002
Jones polynomial of knots formed by repeated tangle replacement operations. Zbl 1207.57010
Diao, Y.; Ernst, C.; Ziegler, U.
7
2009
Generating equilateral random polygons in confinement. Zbl 1229.57004
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
7
2011
Asymptotic bounds on the integrity of graphs and separator theorems for graphs. Zbl 1193.05103
Benko, D.; Ernst, C.; Lanphier, D.
7
2009
Generating equilateral random polygons in confinement. III. Zbl 1320.60034
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
7
2012
Numerical upper bounds on ropelengths of large physical knots. Zbl 1092.57004
Diao, Y.; Ernst, C.; Kavuluru, V.; Ziegler, U.
6
2006
The linking probability for 2-component links which span a lattice tube. Zbl 1185.82008
Atapour, M.; Soteros, C. E.; Ernst, C.; Whittington, S. G.
6
2010
A diagrammatic approach for determining the braid index of alternating links. Zbl 1472.57003
Diao, Yuanan; Ernst, Claus; Hetyei, Gabor; Liu, Pengyu
6
2021
The knot spectrum of confined random equilateral polygons. Zbl 1412.92086
Diao, Y.; Ernst, C.; Montemayor, A.; Rawdon, E.; Ziegler, U.
5
2014
A partial ordering of knots and links through diagrammatic unknotting. Zbl 1200.57004
Diao, Yuanan; Ernst, Claus; Stasiak, Andrzej
5
2009
The mean squared writhe of alternating random knot diagrams. Zbl 1210.57005
Diao, Y.; Ernst, C.; Hinson, K.; Ziegler, U.
5
2010
The linearity of the ropelengths of Conway algebraic knots in terms of their crossing numbers. Zbl 1261.57002
Diao, Yuanan; Ernst, Claus; Ziegler, Uta
5
2011
Tangle equations. II. Zbl 0878.57006
Ernst, C.
5
1997
Total curvature, ropelength and crossing number of thick knots. Zbl 1158.57007
Diao, Y.; Ernst, C.
5
2007
The ropelengths of knots are almost linear in terms of their crossing numbers. Zbl 1441.57006
Diao, Yuanan; Ernst, Claus; Por, Attila; Ziegler, Uta
5
2019
Realizable powers of ropelengths by non-trivial knot families. Zbl 1067.57002
Diao, Yuanan; Ernst, Claus
4
2004
Generating random walks and polygons with stiffness in confinement. Zbl 1318.60051
Diao, Y.; Ernst, C.; Saarinen, S.; Ziegler, U.
4
2015
Generating large random knot projections. Zbl 1106.57005
Diao, Yuanan; Ernst, Claus; Ziegler, Uta
4
2005
Properties of knot energies. Zbl 0932.57009
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
4
1998
In search of a good polygonal knot energy. Zbl 0889.57004
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
4
1997
The knot spectrum of random knot spaces. Zbl 1420.57019
Diao, Yuanan; Ernst, Claus; Ziegler, Uta; Rawdon, Eric J.
3
2018
Nullification numbers of knots with up to 10 crossings. Zbl 1350.57006
Ernst, Claus; Montemayor, Anthony
3
2016
Hamiltonian cycles and rope lengths of Conway algebraic knots. Zbl 1088.57005
Diao, Yuanan; Ernst, Claus
3
2006
Knots with minimal energies. Zbl 0945.57005
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
3
1998
The integrity of small cage graphs. Zbl 1179.05063
Atici, M.; Crawford, R.; Ernst, C.
3
2009
Total curvature and total torsion of knotted random polygons in confinement. Zbl 1422.57019
Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta
2
2018
Relative frequencies of alternating and nonalternating prime knots and composite knots in random knot spaces. Zbl 1420.57018
Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta
2
2018
New upper bounds for the integrity of cubic graphs. Zbl 1060.05060
Atici, M.; Crawford, R.; Ernst, C.
2
2004
The average crossing number of Gaussian random walks and polygons. Zbl 1104.57005
Diao, Yuanan; Ernst, Claus
2
2005
On the range of possible integrities of graphs \(G(n, k)\). Zbl 1234.05141
Atici, Mustafa; Ernst, Claus
2
2011
Average crossing number, total curvature and ropelength of thick knots. Zbl 1261.57003
Ernst, C.; Por, A.
2
2012
Knots with equal bridge index and braid index. Zbl 07478464
Diao, Yuanan; Ernst, Claus; Reiter, Philipp
2
2021
Invariants of rational links represented by reduced alternating diagrams. Zbl 07267542
Diao, Yuanan; Ernst, Claus; Hetyei, Gábor
2
2020
Incoherent nullification of torus knots and links. Zbl 1422.57011
Bettersworth, Zac; Ernst, Claus
1
2019
Nullification of torus knots and links. Zbl 1307.57005
Ernst, Claus; Montemayor, Anthony
1
2014
Ropelengths of closed braids. Zbl 1129.57008
Diao, Yuanan; Ernst, Claus
1
2007
Curvature of random walks and random polygons in confinement. Zbl 1277.82050
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
1
2013
The growth rate of some deficiency zero knot classes. Zbl 1083.57006
Diao, Yuanan; Ernst, Claus
1
2005
Knotting spectrum of polygonal knots in extreme confinement. Zbl 1519.57006
Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta
1
2021
A minimal link on the cubic lattice. Zbl 0998.57012
Ernst, C.; Phipps, M.
1
2002
The crossing numbers of thick knots and links. Zbl 1014.57006
Diao, Yuanan; Ernst, Claus
1
2002
Families of curly knots. Zbl 1516.57006
Ernst, C.; Gover, S.
1
2022
Families of curly knots. Zbl 1516.57006
Ernst, C.; Gover, S.
1
2022
A diagrammatic approach for determining the braid index of alternating links. Zbl 1472.57003
Diao, Yuanan; Ernst, Claus; Hetyei, Gabor; Liu, Pengyu
6
2021
Knots with equal bridge index and braid index. Zbl 07478464
Diao, Yuanan; Ernst, Claus; Reiter, Philipp
2
2021
Knotting spectrum of polygonal knots in extreme confinement. Zbl 1519.57006
Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta
1
2021
Invariants of rational links represented by reduced alternating diagrams. Zbl 07267542
Diao, Yuanan; Ernst, Claus; Hetyei, Gábor
2
2020
The ropelengths of knots are almost linear in terms of their crossing numbers. Zbl 1441.57006
Diao, Yuanan; Ernst, Claus; Por, Attila; Ziegler, Uta
5
2019
Incoherent nullification of torus knots and links. Zbl 1422.57011
Bettersworth, Zac; Ernst, Claus
1
2019
The knot spectrum of random knot spaces. Zbl 1420.57019
Diao, Yuanan; Ernst, Claus; Ziegler, Uta; Rawdon, Eric J.
3
2018
Total curvature and total torsion of knotted random polygons in confinement. Zbl 1422.57019
Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta
2
2018
Relative frequencies of alternating and nonalternating prime knots and composite knots in random knot spaces. Zbl 1420.57018
Diao, Yuanan; Ernst, Claus; Rawdon, Eric J.; Ziegler, Uta
2
2018
Nullification numbers of knots with up to 10 crossings. Zbl 1350.57006
Ernst, Claus; Montemayor, Anthony
3
2016
Generating random walks and polygons with stiffness in confinement. Zbl 1318.60051
Diao, Y.; Ernst, C.; Saarinen, S.; Ziegler, U.
4
2015
The knot spectrum of confined random equilateral polygons. Zbl 1412.92086
Diao, Y.; Ernst, C.; Montemayor, A.; Rawdon, E.; Ziegler, U.
5
2014
Nullification of torus knots and links. Zbl 1307.57005
Ernst, Claus; Montemayor, Anthony
1
2014
Curvature of random walks and random polygons in confinement. Zbl 1277.82050
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
1
2013
Nullification of knots and links. Zbl 1241.57005
Diao, Yuanan; Ernst, Claus; Montemayor, Anthony
10
2012
Generating equilateral random polygons in confinement. II. Zbl 1320.60033
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
9
2012
Generating equilateral random polygons in confinement. III. Zbl 1320.60034
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
7
2012
Average crossing number, total curvature and ropelength of thick knots. Zbl 1261.57003
Ernst, C.; Por, A.
2
2012
Generating equilateral random polygons in confinement. Zbl 1229.57004
Diao, Y.; Ernst, C.; Montemayor, A.; Ziegler, U.
7
2011
The linearity of the ropelengths of Conway algebraic knots in terms of their crossing numbers. Zbl 1261.57002
Diao, Yuanan; Ernst, Claus; Ziegler, Uta
5
2011
On the range of possible integrities of graphs \(G(n, k)\). Zbl 1234.05141
Atici, Mustafa; Ernst, Claus
2
2011
The linking probability for 2-component links which span a lattice tube. Zbl 1185.82008
Atapour, M.; Soteros, C. E.; Ernst, C.; Whittington, S. G.
6
2010
The mean squared writhe of alternating random knot diagrams. Zbl 1210.57005
Diao, Y.; Ernst, C.; Hinson, K.; Ziegler, U.
5
2010
Jones polynomial of knots formed by repeated tangle replacement operations. Zbl 1207.57010
Diao, Y.; Ernst, C.; Ziegler, U.
7
2009
Asymptotic bounds on the integrity of graphs and separator theorems for graphs. Zbl 1193.05103
Benko, D.; Ernst, C.; Lanphier, D.
7
2009
A partial ordering of knots and links through diagrammatic unknotting. Zbl 1200.57004
Diao, Yuanan; Ernst, Claus; Stasiak, Andrzej
5
2009
The integrity of small cage graphs. Zbl 1179.05063
Atici, M.; Crawford, R.; Ernst, C.
3
2009
Total curvature, ropelength and crossing number of thick knots. Zbl 1158.57007
Diao, Y.; Ernst, C.
5
2007
Ropelengths of closed braids. Zbl 1129.57008
Diao, Yuanan; Ernst, Claus
1
2007
Numerical upper bounds on ropelengths of large physical knots. Zbl 1092.57004
Diao, Y.; Ernst, C.; Kavuluru, V.; Ziegler, U.
6
2006
Hamiltonian cycles and rope lengths of Conway algebraic knots. Zbl 1088.57005
Diao, Yuanan; Ernst, Claus
3
2006
Generating large random knot projections. Zbl 1106.57005
Diao, Yuanan; Ernst, Claus; Ziegler, Uta
4
2005
The average crossing number of Gaussian random walks and polygons. Zbl 1104.57005
Diao, Yuanan; Ernst, Claus
2
2005
The growth rate of some deficiency zero knot classes. Zbl 1083.57006
Diao, Yuanan; Ernst, Claus
1
2005
Hamiltonian knot projections and lengths of thick knots. Zbl 1040.57004
Diao, Yuanan; Ernst, Claus; Yu, Xingxing
11
2004
Realizable powers of ropelengths by non-trivial knot families. Zbl 1067.57002
Diao, Yuanan; Ernst, Claus
4
2004
New upper bounds for the integrity of cubic graphs. Zbl 1060.05060
Atici, M.; Crawford, R.; Ernst, C.
2
2004
The linear growth in the lengths of a family of thick knots. Zbl 1046.57006
Diao, Y.; Ernst, C.; Thistlethwaite, M.
11
2003
Upper bounds on linking numbers of thick lines. Zbl 0998.57013
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
9
2002
A minimal link on the cubic lattice. Zbl 0998.57012
Ernst, C.; Phipps, M.
1
2002
The crossing numbers of thick knots and links. Zbl 1014.57006
Diao, Yuanan; Ernst, Claus
1
2002
\(N\)-string tangles. Zbl 1001.57009
Emert, J.; Ernst, C.
10
2000
Thickness of knots. Zbl 0924.57010
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
22
1999
Solving tangle equations arising in a DNA recombination model. Zbl 0916.57013
Ernst, C.; Sumners, D. W.
18
1999
The complexity of lattice knots. Zbl 0924.57007
Diao, Y.; Ernst, C.
19
1998
Properties of knot energies. Zbl 0932.57009
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
4
1998
Knots with minimal energies. Zbl 0945.57005
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
3
1998
Knot energies by ropes. Zbl 0889.57005
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
11
1997
Tangle equations. II. Zbl 0878.57006
Ernst, C.
5
1997
In search of a good polygonal knot energy. Zbl 0889.57004
Diao, Y.; Ernst, C.; Janse van Rensburg, E. J.
4
1997
Tangle equations. Zbl 0857.57005
Ernst, C.
14
1996
A calculus for rational tangles: Applications to DNA recombination. Zbl 0727.57005
Ernst, C.; Sumners, D. W.
50
1990
The growth of the number of prime knots. Zbl 0632.57007
Ernst, C.; Sumners, D. W.
33
1987
all top 5

Cited by 247 Authors

25 Ernst, Claus
23 Diao, Yuanan
11 Rawdon, Eric J.
9 Darcy, Isabel K.
8 Kauffman, Louis Hirsch
7 Simon, Jonathan K.
6 Kwon, Bo-Hyun
6 Orlandini, Enzo
6 Whittington, Stuart G.
6 Ziegler, Uta
5 Cabrera-Ibarra, Hugo
5 Vazquez, Mariel
4 Cantarella, Jason H.
4 Hetyei, Gábor
4 Kim, Hyoungjun
4 Lambropoulou, Sofia S. F.
4 Montemayor, Anthony
4 Panagiotou, Eleni
4 Stoimenow, Alexander
3 Buck, Dorothy
3 Buck, Gregory R.
3 Durumeric, Oguz C.
3 Ishihara, Kai
3 Kanenobu, Taizo
3 Lizárraga Navarro, David A.
3 Moriuchi, Hiromasa
3 No, Sungjong
3 Oh, Seungsang
3 Reiter, Philipp
3 Shonkwiler, Clayton
2 Arsuaga, Javier
2 Bapat, Ravindra Bhalchandra
2 Denne, Elizabeth
2 Dennis, Mark R.
2 Dunkum, Molly W.
2 Even-Zohar, Chaim
2 Ferrari, Franco
2 Fujita, Shinya
2 Hajij, Mustafa
2 Hong, Kyungpyo
2 Huh, Youngsik
2 Janse van Rensburg, Esaias J.
2 Jin, Xian’an
2 Kang, Sungmo
2 Klotz, Alexander R.
2 Kozai, Kenji
2 Lanphier, Dominic
2 Legay, Sylvain
2 Lomonaco, Samuel J. jun.
2 Manoussakis, Yannis G.
2 Matsui, Yasuko
2 Micheletti, Cristian
2 Millett, Kenneth C.
2 Moore, Allison H.
2 Nogueira, João Miguel
2 Pór, Attila
2 Price, Candice Reneé
2 Ramírez Alfonsín, Jorge Luis
2 Ray, Dawn
2 Sakuma, Tadashi
2 Salgueiro, António M.
2 Sazdanović, Radmila
2 Shimokawa, Koya
2 Suzuki, Masaaki
2 Taylor, Alexander John
2 Thistlethwaite, Morwen B.
2 Tuza, Zsolt
2 von der Mosel, Heiko
2 Żak, Andrzej
2 Zhang, Fuji
2 Zhao, Yani
1 Adorisio, Matteo
1 Aguillon, Yasmin
1 Alexander, Keith
1 Alvarado, Sotero
1 Atapour, Mahshid
1 Atici, Mustafa
1 Avvakumov, Sergey Ya.
1 Baker, Kenneth L.
1 Baldwin, Quenisha
1 Baranska, Justyna
1 Bataineh, Khaled
1 Bettersworth, Zac
1 Bodner, Mark
1 Bonato, Anthony
1 Brooks, Susan C.
1 Bryson, Steve
1 Buchanan, Lizzie
1 Burkholder, Eric
1 Bykova, Valentina Vladimirovna
1 Calvo, Jorge Alberto
1 Caraglio, Michele
1 Carr Haden, John
1 Castrillón López, Marco
1 Celani, Antonio
1 Chapman, Harrison
1 Cheng, Xingyu
1 Cohen, Moshe
1 Dabkowski, Mieczysław K.
1 Das, Arindam K.
...and 147 more Authors
all top 5

Cited in 62 Serials

61 Journal of Knot Theory and its Ramifications
20 Topology and its Applications
11 Journal of Physics A: Mathematical and Theoretical
7 Algebraic & Geometric Topology
5 Experimental Mathematics
4 Discrete Applied Mathematics
4 Journal of Statistical Physics
3 Journal of Mathematical Physics
3 Journal of Statistical Mechanics: Theory and Experiment
2 Journal of Computational Physics
2 The Mathematical Intelligencer
2 Proceedings of the American Mathematical Society
2 Graphs and Combinatorics
2 Combinatorics, Probability and Computing
2 Boletín de la Sociedad Matemática Mexicana. Third Series
2 Journal of Mathematical Chemistry
2 The European Physical Journal B. Condensed Matter and Complex Systems
2 Involve
1 Archive for Rational Mechanics and Analysis
1 Computers & Mathematics with Applications
1 Communications on Pure and Applied Mathematics
1 Discrete Mathematics
1 International Journal of Theoretical Physics
1 Journal of Mathematical Biology
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Nuclear Physics. B
1 Physica A
1 Physics Letters. A
1 Physics Reports
1 Reviews of Modern Physics
1 Theoretical and Mathematical Physics
1 Bulletin of Mathematical Biology
1 Chaos, Solitons and Fractals
1 Applied Mathematics and Computation
1 Canadian Journal of Mathematics
1 Fundamenta Mathematicae
1 Journal of Algebra
1 Mathematische Annalen
1 Mathematische Nachrichten
1 Networks
1 Osaka Journal of Mathematics
1 Transactions of the American Mathematical Society
1 European Journal of Combinatorics
1 Advances in Applied Mathematics
1 Journal of Symbolic Computation
1 Mathematical and Computer Modelling
1 SIAM Journal on Discrete Mathematics
1 International Journal of Mathematics
1 The Annals of Applied Probability
1 Differential Geometry and its Applications
1 Proceedings of the National Academy of Sciences of the United States of America
1 Bulletin of the American Mathematical Society. New Series
1 Topology Proceedings
1 Russian Journal of Mathematical Physics
1 The Electronic Journal of Combinatorics
1 Acta Mathematica Sinica. English Series
1 Mediterranean Journal of Mathematics
1 Symmetry
1 Journal of Theoretical Biology
1 Journal of Applied and Computational Topology
1 Computational and Mathematical Biophysics
1 Prikladnaya Diskretnaya Matematika

Citations by Year