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References

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A

  • Andruskiewitsch, Nicolás, Graña, Matías. From racks to pointed Hopf algebras. Adv. Math. 178 (2003), no. 2, 177--243. MR1994219 (2004i:16046)

B

  • Bartholomew, Andrew; Fenn, Roger. Biquandles of small size and some invariants of virtual and welded knots. J. Knot Theory Ramifications 20 (2011), no. 7, 943--954. MR2819176 (2012e:57004)

  • Bojarczuk, Joaquim; Lopes, Pedro. Quandles at finite temperatures. III. J. Knot Theory Ramifications 14 (2005), no. 3, 275--373. MR2149512 (2006b:57034)

  • Brieskorn, E. Automorphic sets and braids and singularities. Braids (Santa Cruz, CA, 1986), 45--115, Contemp. Math., 78, Amer. Math. Soc., Providence, RI, 1988. MR0975077 (90a:32024)

C

  • Carter, J. Scott. A survey of quandle ideas. Introductory lectures on knot theory, 22--53, Ser. Knots Everything, 46, World Sci. Publ., Hackensack, NJ, 2012. MR2885229

  • Carter, J. Scott; Oshiro, Kanako; Saito, Masahico. Symmetric extensions of dihedral quandles and triple points of non-orientable surfaces. Topology Appl. 157 (2010), no. 5, 857--869. MR2593699 (2011c:57034)

  • Carter, J. Scott; Elhamdadi, Mohamed; Graña, Matias; Saito, Masahico. Cocycle knot invariants from quandle modules and generalized quandle homology. Osaka J. Math. 42 (2005), no. 3, 499--541. MR2166720 (2006d:57017)

  • Carter, J. Scott; Jelsovsky, Daniel; Kamada, Seiichi; Langford, Laurel; Saito, Masahico. Quandle cohomology and state-sum invariants of knotted curves and surfaces. Trans. Amer. Math. Soc. 355 (2003), no. 10, 3947--3989. MR1990571 (2005b:57048)

  • Carter, J. Scott; Jelsovsky, Daniel; Kamada, Seiichi; Saito, Masahico. Quandle homology groups, their Betti numbers, and virtual knots. J. Pure Appl. Algebra 157 (2001), no. 2-3, 135--155. MR1812049 (2002f:57010)

  • Clauwens, Frans. The algebra of rack and quandle cohomology. J. Knot Theory Ramifications 20 (2011), no. 11, 1487--1535. MR2854230 (2012k:18022)

  • Ceniceros, Jessica; Nelson, Sam. Twisted virtual biracks and their twisted virtual link invariants. Topology Appl. 160 (2013), no. 2, 421--429. MR3003341

D

  • Dionísio, F. Miguel; Lopes, Pedro. Quandles at finite temperatures. II. J. Knot Theory Ramifications 12 (2003), no. 8, 1041--1092. MR2017983 (2004j:57015)

E

  • Etingof, P.; Graña, M. On rack cohomology. J. Pure Appl. Algebra 177 (2003), no. 1, 49--59. MR1948837 (2004e:55006)

  • Etingof, Pavel; Schedler, Travis; Soloviev, Alexandre. Set-theoretical solutions to the quantum Yang-Baxter equation. Duke Math. J. 100 (1999), no. 2, 169--209. MR1722951 (2001c:16076)

  • Etingof, Pavel; Soloviev, Alexander; Guralnick, Robert. Indecomposable set-theoretical solutions to the quantum Yang-Baxter equation on a set with a prime number of elements. J. Algebra 242 (2001), no. 2, 709--719. MR1848966 (2002e:20049)

F

  • Fenn, Roger; Rourke, Colin; Sanderson, Brian. The rack space. Trans. Amer. Math. Soc. 359 (2007), no. 2, 701--740 (electronic). MR2255194 (2007g:55013)

  • Fenn, Roger; Rourke, Colin; Sanderson, Brian. An introduction to species and the rack space. Topics in knot theory (Erzurum, 1992), 33--55, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 399, Kluwer Acad. Publ., Dordrecht, 1993. MR1257904

  • Fenn, Roger; Rourke, Colin. Racks and links in codimension two. J. Knot Theory Ramifications 1 (1992), no. 4, 343--406. MR1194995 (94e:57006)

G

  • Graña, Matías. Indecomposable racks of order $p\sp 2$. Beiträge Algebra Geom. 45 (2004), no. 2, 665--676. MR2093034 (2005k:57025)

H

  • Henderson, Richard; Macedo, Todd; Nelson, Sam. Symbolic computation with finite quandles. J. Symbolic Comput. 41 (2006), no. 7, 811--817. MR2232202 (2007a:68080)

  • Hou, Xiang-dong. Automorphism groups of Alexander quandles. J. Algebra 344 (2011), 373--385. MR2831947 (2012j:20186)

J

  • Joyce, David. Simple quandles. J. Algebra 79 (1982), no. 2, 307--318. MR0682881 (84d:20078)

  • Joyce, David. A classifying invariant of knots, the knot quandle. J. Pure Appl. Algebra 23 (1982), no. 1, 37--65. MR0638121 (83m:57007)

K

  • Kamada, Seiichi. Quandles and knot invariants. (Japanese) Sūgaku 64 (2012), no. 3, 304--324. MR2978543

  • Kamada, Naoko. Polynomial invariants and quandles of twisted links. Topology Appl. 159 (2012), no. 4, 999--1006. MR2876706 (Reviewed)

  • Kamada, Seiichi; Oshiro, Kanako. Homology groups of symmetric quandles and cocycle invariants of links and surface-links. Trans. Amer. Math. Soc. 362 (2010), no. 10, 5501--5527. MR2657689 (2011f:57017)

L

  • Litherland, R. A.; Nelson, Sam. The Betti numbers of some finite racks. J. Pure Appl. Algebra 178 (2003), no. 2, 187--202. MR1952425 (2004a:57006)

  • Lopes, Pedro; Roseman, Dennis. On finite racks and quandles. Comm. Algebra 34 (2006), no. 1, 371--406. MR2194774 (2006h:57010)

  • Lopes, Pedro. Quandles at finite temperatures. I. J. Knot Theory Ramifications 12 (2003), no. 2, 159--186. MR1967239 (2004b:57021)

M

  • Matveev, S. V. Distributive groupoids in knot theory. (Russian) Mat. Sb. (N.S.) 119(161) (1982), no. 1, 78--88, 160. MR0672410 (84e:57008)

  • Mochizuki, Takuro. The third cohomology groups of dihedral quandles. J. Knot Theory Ramifications 20 (2011), no. 7, 1041--1057. MR2819181 (2012e:18028)

  • Mochizuki, Takuro. The 3-cocycles of the Alexander quandles $\Bbb F\sb qT/(T-\omega)$. Algebr. Geom. Topol. 5 (2005), 183--205 (electronic). MR2135551 (2006e:57019)

  • Mochizuki, Takuro. Some calculations of cohomology groups of finite Alexander quandles. J. Pure Appl. Algebra 179 (2003), no. 3, 287--330. MR1960136 (2004b:55013)

  • Murillo, Gabriel; Nelson, Sam. Erratum: Alexander quandles of order 16 MR2402506. J. Knot Theory Ramifications 18 (2009), no. 5, 727. MR2527683 (2010g:57005)

  • Lam, Daisy; Nelson, Sam. An isomorphism theorem for Alexander biquandles. Internat. J. Math. 20 (2009), no. 1, 97--107. MR2488716 (2009m:57023)

  • Murillo, Gabriel; Nelson, Sam. Alexander quandles of order 16. J. Knot Theory Ramifications 17 (2008), no. 3, 273--278. MR2402506 (2009e:57013)

N

  • Navas, Esteban Adam; Nelson, Sam. On symplectic quandles. Osaka J. Math. 45 (2008), no. 4, 973--985. MR2493966 (2009m:20098)

  • Nelson, Sam. A polynomial invariant of finite quandles. J. Algebra Appl. 7 (2008), no. 2, 263--273. MR2417045 (2009b:57029)

  • Nelson, Sam. Generalized quandle polynomials. Canad. Math. Bull. 54 (2011), no. 1, 147--158. MR2797975 (Reviewed)

  • Nelson, Sam. A polynomial invariant of finite quandles. J. Algebra Appl. 7 (2008), no. 2, 263--273. MR2417045 (2009b:57029)

  • Nelson, Sam. Classification of finite Alexander quandles. Proceedings of the Spring Topology and Dynamical Systems Conference. Topology Proc. 27 (2003), no. 1, 245--258. MR2048935 (2005b:57027)

  • Niebrzydowski, Maciej; Przytycki, Józef H. The second quandle homology of the Takasaki quandle of an odd abelian group is an exterior square of the group. J. Knot Theory Ramifications 20 (2011), no. 1, 171--177. MR2777023 (2012g:55009)

  • Niebrzydowski, M.; Przytycki, J. H. Homology operations on homology of quandles. J. Algebra 324 (2010), no. 7, 1529--1548. MR2673749 (2012b:55009)

  • Niebrzydowski, Maciej; Przytycki, Józef H. The quandle of the trefoil knot as the Dehn quandle of the torus. Osaka J. Math. 46 (2009), no. 3, 645--659. MR2583322 (2010j:57008)

S

  • Soloviev, Alexander. Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation. Math. Res. Lett. 7 (2000), no. 5-6, 577--596. MR1809284 (2001h:16048)

T

V

  • Vendramin, L. On the classification of quandles of low order. J. Knot Theory Ramifications 21 (2012), no. 9, 1250088, 10 pp. MR2926571
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