EN
IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS
Abstract
Anderson and Harary introduced two impartial games on finite
groups. Both games are played by two players who alternately select previouslyunselected
elements of a finite group. The first player who builds a generating
set from the jointly-selected elements wins the first game. The first player
who cannot select an element without building a generating set loses the second
game. We determine the nim-numbers, and therefore the outcomes, of
these games for symmetric and alternating groups.
Keywords
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
-
Publication Date
December 1, 2016
Submission Date
December 1, 2016
Acceptance Date
-
Published in Issue
Year 2016 Volume: 20 Number: 20
APA
Benesh, B. J., Ernst, D. C., & Sieben, N. (2016). IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS. International Electronic Journal of Algebra, 20(20), 70-85. https://doi.org/10.24330/ieja.266184
AMA
1.Benesh BJ, Ernst DC, Sieben N. IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS. IEJA. 2016;20(20):70-85. doi:10.24330/ieja.266184
Chicago
Benesh, Bret J., Dana C. Ernst, and Nandor Sieben. 2016. “IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS”. International Electronic Journal of Algebra 20 (20): 70-85. https://doi.org/10.24330/ieja.266184.
EndNote
Benesh BJ, Ernst DC, Sieben N (December 1, 2016) IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS. International Electronic Journal of Algebra 20 20 70–85.
IEEE
[1]B. J. Benesh, D. C. Ernst, and N. Sieben, “IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS”, IEJA, vol. 20, no. 20, pp. 70–85, Dec. 2016, doi: 10.24330/ieja.266184.
ISNAD
Benesh, Bret J. - Ernst, Dana C. - Sieben, Nandor. “IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS”. International Electronic Journal of Algebra 20/20 (December 1, 2016): 70-85. https://doi.org/10.24330/ieja.266184.
JAMA
1.Benesh BJ, Ernst DC, Sieben N. IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS. IEJA. 2016;20:70–85.
MLA
Benesh, Bret J., et al. “IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS”. International Electronic Journal of Algebra, vol. 20, no. 20, Dec. 2016, pp. 70-85, doi:10.24330/ieja.266184.
Vancouver
1.Bret J. Benesh, Dana C. Ernst, Nandor Sieben. IMPARTIAL AVOIDANCE AND ACHIEVEMENT GAMES FOR GENERATING SYMMETRIC AND ALTERNATING GROUPS. IEJA. 2016 Dec. 1;20(20):70-85. doi:10.24330/ieja.266184
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