Gröbner bases and the number of Latin squares related to autotopisms of order ≤7

Journal of Symbolic Computation

Volumn 42, Issue 11-12, 2007, Pages 1142-1154

  Falcon R M ^a   Martin Morales J ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Autotopism group; Gr bner basis; Latin square

Indexed keywords

EID: 35848930389     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2007.07.004     Document Type: Article

References (13)

1. Adams W., and Loustaunau P. An Introduction to Gröbner Bases. Graduate Studies in Mathematics vol. 3 (1994), American Mathematical Society, Providence, RI
2. Albert A.A. Quasigroups I. Transactions of the American Mathematical Society 54 (1943) 507-519
3. Bayer, D., 1982. The division algorithm and the Hilbert scheme. Ph. D. Thesis. Harvard University
4. Bruck R.H. Some results in the theory of quasigroups. Transactions of the American Mathematical Society 55 (1944) 19-54
5. Buchberger, B., 1965. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph. D. Thesis. University of Innsbruck. English translation 2006: An algorithm for finding the basis elements in the residue class ring modulo a zero dimensional polynomial ideal. (Logic, mathematics, and computer science: Interactions). Journal of Symbolic Computation. 41 (3-4), 475-511 (special issue)
6. Cox D., Little J., and O'Shea D. Ideals, Varieties and Algorithms (1997), Springer, Berlin
7. Falcón, R.M., 2006. Latin squares associated to principal autotopisms of long cycles. Application in Cryptography. In: Proceedings of Transgressive Computing 2006: A Conference in Honor of Jean Della Dora. Granada. pp. 213-230
8. Falcón, R.M., 2007. Cycle structures of autotopisms of the Latin squares of order up to 11. Ars Combinatoria (in press). http://arxiv.org/abs/0709.2973
9. Gago-Vargas J., Hartillo-Hermoso I., Martín-Morales J., and Ucha-Enríquez J.M. Sudokus and Gröbner bases not only a divertimento. CASC 2006. Lecture Notes in Computer Science vol. 4194 (2006) 155-165
10. Greuel, G.-M., Pfister, G., Schönemann, H., 2005. Singular 3.0. A computer algebra system for polynomial computations. Centre for Computer Algebra, University of Kaiserlautern. http://www.singular.uni-kl.de
11. Laywine C.F., and Mullen G.L. Discrete Mathematics Using Latin Squares. Series in Discrete Mathematics and Optimization (1998), Wiley-Interscience. 0-471-24064-8
12. Martín-Morales, J., 2006. Sudoku and Gröbner bases. In: Proceedings of Transgressive Computing 2006: A Conference in Honor of Jean Della Dora. Granada. pp. 303-310
13. McKay B.D., Meynert A., and Myrvold W. Small Latin squares, quasigroups and loops. Journal of Combinatorial Designs 15 (2007) 98-119