Physical Sciences and Mathematics Commons^™

The Spectrum Of Nim-Values For Achievement Games For Generating Finite Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Mathematics Faculty Publications

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 {0, 1, 2, 3, 4}. This positively answers two conjectures from a previous paper by the last two authors.

How Effective Is The Efficiency Gap?, Thomas Q. Sibley

Mathematics Faculty Publications

Gerrymandering has affected U. S. politics since at least 1812. A political cartoon that year decried this tactic by then Massachusetts Governor Elbridge Gerry. (Gerrymandering is manipulating the boundaries of districts to benefit a group unfairly.)

While we may feel we know a gerrymander when we see one, finding a meaningful metric has proven challenging. This article uses elementary mathematics to investigate the efficiency gap, a recent model proposed to measure gerrymandering.