Albion College
Mathematics and Computer Science
COLLOQUIUM
Reducibility and Balanced Intransitive Dice
Michael Ivanitskiy1 and Michael A. Jones2

1University of Michigan; 2Mathematical Reviews

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.
3:30 PM
All are welcome!
Palenske 227
September 27, 2018