ENUMERATION OF SET-THEORETIC SOLUTIONS TO THE YANG-BAXTER EQUATION

被引：10

作者：

Akgun, O. ^{[1
]}

Mereb, M. ^{[2
,3
]}

Vendramin, L. ^{[2
,3
,4
]}

机构：

[1] Univ St Andrews, Sch Comp Sci, St Andrews KY16 9SX, Fife, Scotland

[2] Univ Buenos Aires, FCEN, CONICET, IMAS, Pab 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina

[3] Univ Buenos Aires, FCEN, Dept Matemat, Pab 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina

[4] Vrije Univ Brussel, Dept Math, Pl Laan 2, B-1050 Brussels, Belgium

来源：

MATHEMATICS OF COMPUTATION | 2022年 / 91卷 / 335期

关键词：

Yang-Baxter; biquandles; constraint programming; SKEW BRACES;

D O I：

10.1090/mcom/3696

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang???Baxter equation of small size. We show that there are 321,931 involutive solutions of size nine, 4,895,272 involutive solutions of size ten and 422,449,480 non-involutive solution of size eight. Our method is then used to enumerate non-involutive biquandles.

引用

页码：1469 / 1481

页数：13

共 41 条

[1] Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces [J].

Acri, E. ;

Lutowski, R. ;

Vendramin, L. .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2020, 30 (01) :91-115

[2]

Ashford M, 2017, ELECTRON J COMB, V24

[3] A family of irretractable square-free solutions of the Yang-Baxter equation [J].

Bachiller, David ;

Cedo, Ferran ;

Jespers, Eric ;

Okninski, Jan .

FORUM MATHEMATICUM, 2017, 29 (06) :1291-1306

[4] BIQUANDLES OF SMALL SIZE AND SOME INVARIANTS OF VIRTUAL AND WELDED KNOTS [J].

Bartholomew, Andrew ;

Fenn, Roger .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2011, 20 (07) :943-954

[5] PARTITION-FUNCTION OF 8-VERTEX LATTICE MODEL [J].

BAXTER, RJ .

ANNALS OF PHYSICS, 1972, 70 (01) :193-&

[6]

Blackburn SR, 2013, ELECTRON J COMB, V20

[7] About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation [J].

Castelli, Marco ;

Catino, Francesco ;

Pinto, Giuseppina .

COMMUNICATIONS IN ALGEBRA, 2020, 48 (06) :2369-2381

[8] Retractability of set theoretic solutions of the Yang-Baxter equation [J].

Cedo, Ferran ;

Jespers, Eric ;

Okninski, Jan .

ADVANCES IN MATHEMATICS, 2010, 224 (06) :2472-2484

[9]

Childs LN, 2019, NEW YORK J MATH, V25, P574

[10] ACTIONS OF SKEW BRACES AND SET-THEORETIC SOLUTIONS OF THE REFLECTION EQUATION [J].

De Commer, K. .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2019, 62 (04) :1089-1113

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