Link to project report (department only)
Keller Hall 413
Elliot Ossanna, Master’s presentation, Monday, April 30, 2018, 10:30 am, Keller 403
Fractal nature of generalized binomial triangles modulo $p$
Abstract: A well-known property of Pascal’s Triangle is that reducing entries modulo a prime yields a fractal, Sierpinski’s Triangle-like pattern. We generalize this to triangles generated by strong divisibility Lucas Sequences, and conclude that the generated fractal is uniquely determined by the prime modulus, not the underlying generating sequence.
Keller Hall 403
Dissertation draft (department only)
Alejandro Guillen, PhD defense, Tuesday, May 1, 2018, 12 noon,
Title: On the Generalized Word Problem for Finitely Presented Lattices”
Abstract: The generalized word problem for a lattice L in a variety V asks if, given a finite
subset Y of L and an element d in L, there is an algorithm to determine if d is in the subalgebra
of L generated by Y. Freese and Nation showed that the generalized word problem for finitely
presented lattices is solvable. This algorithm, though effective, is potentially exponential. We
present a polynomial time algorithm for the generalized word problem for free lattices, but
explain the complications which can arise when trying to adapt this algorithm to the generalized
word problem for finitely presented lattices. Though some of the results for free lattices are
shown to transfer over for finitely presented lattices, we give a potential syntactic algorithm
for the generalized word problem for finitely presented lattices. Finally, we give a new proof
that the generalized word problem for finitely presented lattices is solvable, relying on the
partial completion, PC(P), of a partially defined lattice P.