Seminar Series: Sperner’s Lemma and Connection Games, December 2, 2014

Interdisciplinary Series, Tuesday, December 2, 2014 12:00 – 1:00pm

Location: CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Title: Sperner’s Lemma and Connection Games

Speaker: David Molnar, Rutgers University

Abstract

The game of Hex is the most well-known of the great iceberg of connection games. 119100010_1203624c7a_zis played on a triangular board, with the goal to connect all three sides. A beautiful proof using Sperner’s Lemma shows that the game cannot end in a draw. From this the fact that Hex cannot end in a draw follows as a corollary.

In early 2008, Mark Steere published two new connection games, Atoll and Begird, which generalize Hex and Y, respectively. Atoll has received some attention through online play and a feature in Games magazine. Atoll is played on a grid of hexagons surrounded by eight ‘islands’; the goal is to connect two opposite islands one one’s color. One way to prove that there must be a winner in a game of Atoll, Begird, and in fact infinitely many generalizations, uses a generalized version of Sperner’s Lemma. I will discuss this generalization and its consequences.

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