Androids Armed With Poisoned Chocolate Squares: Ideal Nim and Its Relatives. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Dozier, Haley; Perry, John
• Is Part Of: Mathematics magazine. Volume 89:Issue 4(2016)
• Page Start: 235
• Page End: 250
• Publication Date: 2016-10-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/math.mag.89.4.235
• Languages: English
• ISSNs: 0025-570X

Abstract

Summary: We describe two new combinatorial games. The first, Ideal Nim, both generalizes the well-known game Nim and its relative Chomp, and provides a recreational perspective on some important ideas of commutative algebra; for instance, the fact that the game is guaranteed to end is equivalent to Dickson's lemma, a well-known fact of commutative algebra. This relationship leads to a game-based proof of Dickson's lemma. The second game, Gröbner Nim, is really a variant of Ideal Nim that illustrates Buchberger's algorithm to compute a Gröbner basis. We conclude by describing the relationship between Gröbner Nim and polynomial rings.