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Maximum arrangements of nonattacking kings on the chessboard
Tricia Muldoon Brown
To count the number of maximum independent arrangements of kings on a chessboard, we build a matrix whose entries are independent arrangement…
The Problem of Pawns
Tricia Muldoon Brown
Using a bijective proof, we show the number of ways to arrange a maximum number of nonattacking pawns on a chessboard is , and more generally, the nu…
On the unimodality of convolutions of sequences of binomial coefficients
Tricia Muldoon Brown
We provide necessary and sufficient conditions on the unimodality of a convolution of two sequences of binomial coefficients preceded by a finite number of ones. These convolution…
Convex domino towers
Tricia Muldoon Brown
We study convex domino towers using a classic dissection technique on polyominoes to find the generating function and an asymptotic approximation.
On the enumeration of k-omino towers
Tricia Muldoon Brown
We describe a class of fixed polyominoes called -omino towers that are created by stacking rectangular blocks of size on a convex base composed of these same -omi…
Exploring mod2 n-queens games
Tricia Muldoon Brown, Abrahim Ladha
We introduce a two player game on an n x n chessboard where queens are placed by alternating turns on a chessboard square whose availability is determined by the number of queens a…