3 papers
math.CO2019
A Graph Theory of Rook Placements
Kenneth Barrese
Two boards are rook equivalent if they have the same number of non-attacking rook placements for any number of rooks. Define a rook equivalence graph of an equivalence set of Ferre…
math.CO2015
Bijections on m-level Rook Placements
Kenneth Barrese, Nicholas Loehr, Jeffrey Remmel +1
Suppose the rows of a board are partitioned into sets of m rows called levels. An m-level rook placement is a subset of the board where no two squares are in the same column or the…
math.CO2013
m-Level rook placements
Kenneth Barrese, Nicholas Loehr, Jeffrey Remmel +1
Goldman, Joichi, and White proved a beautiful theorem showing that the falling factorial generating function for the rook numbers of a Ferrers board factors over the integers. Brig…