4 papers
Unimodal Polynomials and Lattice Walk Enumeration with Experimental Mathematics
Bryan Ek
The main theme of this dissertation is retooling methods to work for different situations. I have taken the method derived by O'Hara and simplified by Zeilberger to prove unimodali…
Lattice Walk Enumeration
Bryan Ek
Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool…
q-Binomials and related symmetric unimodal polynomials
Bryan Ek
The q-binomial coefficients were assumed to be unimodal as early as the 1850's, but it remained unproven until Sylvester's 1878 proof using invariant theory. In 1982, Proctor gave…
Counting Permutations that Avoid Many Patterns
Yonah Biers-Ariel, Haripriya Chakraborty, John Chiarelli +8
This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.