Corey Manack

activity

20102015

collaborators

6 papers

math.DS2015

Digit sequences of rational billiards on tables which tile $R^{2}$

Corey Manack, Marko Savic

We classify the periodic digit strings which arise from periodic billiard orbits on the four convex $n$ -gons $Δ$ which tile $R^{2}$ under reflection, answering problem a pos…

math.HO2015

Taking the risk out of RISK: Conquer Odds in the Board Game RISK

Sam Hendel, Charles Hoffman, Corey Manack +1

Dice odds in the board game RISK were first investigated by Tan, fixed by Osbourne, and extended by Blatt. We generalized dice odds further, varying the number of sides and the num…

math.NT2015

Leading Digit Laws on Linear Lie Groups

Corey Manack, Steven J. Miller

We determine the leading digit laws for the matrix components of a linear Lie group $G$ . These laws generalize the observations that the normalized Haar measure of the Lie group $\…

math.RT2013

Character Estimates of Adjoint Simple Lie Groups

Corey Manack

Call a compact, connected, simple Lie group $G$ {\emph{adjoint simple}} if it has trivial center. Let $C \subset G$ be a nontrivial conjugacy class, $e \in G$ the identity element of…

math.CO2012

Enumeration of k-Exceedance Lattice Paths with an Application to Comparing Chains of Order Statistics

Charles Hoffman, Corey Manack

We enumerate the number of monotonic lattice paths starting at $(0, 0)$ and terminating at $(m, n)$ in which $l$ of the first $k$ steps lie below the line $y=x\ (0\leq k\leq m\leq n)…

math.RT2010

Low Degree Representations of Simple Lie Groups

Robert Guralnick, Michael Larsen, Corey Manack

We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irred…