On the Lucky Sets of Fubini Rankings

Melissa Beerbower
Loyola University Chicago

Recall that Fubini rankings of length n are rankings of n competitors allowing for ties. We can say that the number of rankings, k, with k less than or equal to n, is equal to the number of lucky competitors. A lucky competitor is the first to attain its rank. We enumerate Fubini rankings recursively through fixed sets of lucky competitors. Also recall that unit Fubini rankings are Fubini rankings with at most two competitors for each rank. We enumerate unit Fubini rankings through fixed lucky sets. Our enumerations explain twin coefficients for minimum powers in the lucky polynomial of ell-interval Fubini rankings.