THE SPECTRUM OF NIM-VALUES FOR ACHIEVEMENT GAMES FOR GENERATING FINITE GROUPS

Bret J. Benesh; Dana C. Ernst; Nándor Sieben

doi:10.5281/zenodo.8174526

THE SPECTRUM OF NIM-VALUES FOR ACHIEVEMENT GAMES FOR GENERATING FINITE GROUPS

Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is {1; 2; 3; 4}. This positively answers two conjectures from a previous paper by the last two authors.

Original language	English (US)
Journal	Integers
Volume	23
DOIs	https://doi.org/10.5281/zenodo.8174526
State	Published - 2023

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.5281/zenodo.8174526

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abstract = "We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The game ends when the jointly selected elements generate the group. The last player able to make a move is the winner of the game. We prove that the spectrum of nim-values of these games is {1; 2; 3; 4}. This positively answers two conjectures from a previous paper by the last two authors.",

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THE SPECTRUM OF NIM-VALUES FOR ACHIEVEMENT GAMES FOR GENERATING FINITE GROUPS

Abstract

ASJC Scopus subject areas

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