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We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang-Baxter equation of small size.
Some exact results for the many-body problem in one dimension with repulsive delta-function interaction
C. N. Yang · 1967
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Construction and analysis of non-equivalent finite semigroups
R. Plemmons · 1970
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Partition function of the eight-vertex lattice model
R. J. Baxter · 1972
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On some unsolved problems in quantum group theory
V. G. Drinfel ′ · 1992
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Semigroups of I I -type
T. Gateva-Ivanova and M. Van den Bergh · 1998
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Set-theoretical solutions to the quantum Yang-Baxter equation
P. Etingof, T. Schedler, and A. Soloviev · 1999
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On the set-theoretical Yang-Baxter equation
J.-H. Lu, M. Yan, and Y.-C. Zhu · 2000
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Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation
A. Soloviev · 2000
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Partial symmetry breaking
I. McDonald and B. Smith · 2002
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Survey on matched pairs of groups—an elementary approach to the ESS-LYZ theory
M. Takeuchi · 2003
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A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation
T. Gateva-Ivanova · 2004
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A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
W. Rump · 2005
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Minion: A fast, scalable, constraint solver
I. P. Gent, C. Jefferson, and I. Miguel · 2006
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Matrices and finite biquandles
S. Nelson and J. Vo · 2006
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Essence: A constraint language for specifying combinatorial problems
A. M. Frisch, W. Harvey, C. Jefferson, B. Martínez-Hernández, and I. Miguel · 2008
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Retractability of set theoretic solutions of the Yang-Baxter equation
F. Cedó, E. Jespers, and J. Okniński · 2010
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Biquandles of small size and some invariants of virtual and welded knots
A. Bartholomew and R. Fenn · 2011
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Automatic generation of constraints for partial symmetry breaking
C. Jefferson and K. E. Petrie · 2011
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The Semigroups of Order 10
A. Distler, C. A. Jefferson, T. Kelsey, and L. Kotthoff · 2012
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Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity
T. Gateva-Ivanova · 2012
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Automatically improving constraint models in Savile Row
P. Nightingale, Ö. Akgün, I. P. Gent, C. Jefferson, I. Miguel, and P. Spracklen · 2017
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Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups
T. Gateva-Ivanova · 2018
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On skew braces (with an appendix by N. Byott and L. Vendramin)
A. Smoktunowicz and L. Vendramin · 2018
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Bi-skew braces and Hopf Galois structures
L. N. Childs · 2019
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Actions of skew braces and set-theoretic solutions of the reflection equation
K. De Commer · 2019
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An enumeration process for racks
J. Hoste and P. D. Shanahan · 2019
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Multipermutation solutions of the Yang-Baxter equation
T. Gateva-Ivanova and P. Cameron · 2012
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Enumerating finite racks, quandles and kei
S. R. Blackburn · 2013
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The brace of a classical group
W. Rump · 2014
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Extensions of set-theoretic solutions of the Yang–Baxter equation and a conjecture of Gateva-Ivanova
L. Vendramin · 2016
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Counting racks of order n n
M. Ashford and O. Riordan · 2017
Cited alongside, same era.
A family of irretractable square-free solutions of the Yang-Baxter equation
D. Bachiller, F. Cedó, E. Jespers, and J. Okniński · 2017
Cited alongside, same era.
On structure groups of set-theoretic solutions to the Yang-Baxter equation
V. Lebed and L. Vendramin · 2019
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Left braces and the quantum Yang-Baxter equation
H. Meng, A. Ballester-Bolinches, and R. Esteban-Romero · 2019
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A covering theory for non-involutive set-theoretic solutions to the Yang-Baxter equation
W. Rump · 2019
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Enumeration of racks and quandles up to isomorphism
P. Vojtěchovský and S. Y. Yang · 2019
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Retractability of solutions to the Yang-Baxter equation and p p -nilpotency of skew braces
E. Acri, R. Lutowski, and L. Vendramin · 2020
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About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation
M. Castelli, F. Catino, and G. Pinto · 2020
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GAP – Groups, Algorithms, and Programming, Version 4.11.0
The GAP Group · 2020
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