A generalized quadrangle is a type of geometry that contains within it
no triangles. In particular, we will be considering these structures in the ﬁnite
case. In this thesis, we focus on a particular generalized quadrangle ...
The geometric hyperplanes of generalized quadrangles and their
pairwise intersections are studied using combinatorial techniques. Particular
attention is paid to the family of regular generalized quadrangles W(q), when
q ...
For any real numbers a, b, and c, we form the sequence of polynomials {Pn(z)}∞ n=0 satisfying the four-term recurrence
Pn(z) = −azPn−1(z)−bPn−2(z)−czPn−3(z), n ∈N,
with the initial conditions P0(z) = 1 and P−n(z) = 0. We ...
Sums of powers of integers have been studied extensively for many centuries. The Pythagoreans, Archimedes, Fermat, Pascal, Bernoulli, Faulhaber, and other mathematicians have discovered formulas for sums of powers of the ...
A mathematical braid is a set of strands passing between two parallel
planes in space, such that each strand passes through any parallel plane that
lies between the two planes exactly once. The set of all braids with n ...