Albion College Mathematics and Computer Science Colloquium


Title: Reducibility and Balanced Intransitive Dice
Speaker:Michael Ivanitskiy1 and Michael A. Jones2
1University of Michigan; 2Mathematical Reviews
Ann Arbor, MI
Abstract: We will review some results about balanced intransitive $n$-sided dice and what it means for a set of dice to be reducible based on a concatenation operation. Using data from the Online Encyclopedia of Integer Sequences, the lexicographical ordering of dice, and permutations, we are able to construct new integer sequences representing the number of $n$-sided reducible and irreducible dice. We define a notion of margin and explain how margins are effected by concatenation. We introduce a new splicing operation that generalizes concatenation and give conditions for when the resulting dice are balanced and irreducible. Finally, we construct new integer sequences for the number of fair, balanced dice and the largest margins for $n$-sided, balanced intransitive dice.

Bonus: You will either get to make or will be given a set of balanced, intransitive dice.
Location: Palenske 227
Date:9/27/2018
Time: 3:30 PM 


@abstract{MCS:Colloquium:MichaelIvanitskiy1andMichaelAJones2:2018:9:27,
author  = "{Michael Ivanitskiy1 and Michael A. Jones2}",
title   = "{Reducibility and Balanced Intransitive Dice}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{27 September}",
year    = "{2018}"
}