FINAL Projects for Doron Zeilberger's Spring 2012 EXPERIMENTAL MATHEMATICS Course

First posted: May 6, 2012

Note: Many of the projects here are "work in progress" that will be updated periodically.

• Philip Benjamin and Kristen Lew's project to study tetrahedra with integer sides
  [see: problem description, and for background: Sastry's article about Brahmagupta Quadrilaterals].

• Michael Burkhart's project extending the Sontag-Zeilberger approach
  [here is the background: the Sontag-Zeilberger article "A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions" ]

• Patrick Devlin's project sadly refuting Edinah Gnang's intriguing conjecture (about towers of primes).

• John Kim' project in Extremal Graph Theory
  [outline: Let ex(n,H) be the maximum number of edges in a n vertex graph that does not contain H as a subgraph (i.e. ex(n,H)+1 is the minimum number of edges that guarantees H is a subgraph). Compute seq(ex(n,H),n=1..N) for various graphs H.]

• Neil Lutz is creating a database of sequences counting self-avoiding walks avoiding in addition certain sets as subpaths.
  [Not yet ready to be posted]

• Ben Miles and Alex Gentul's project to study generalizations of alternating permutations
  [for background see wiki entry on alternating permutations They wrote a Maple package to enumerate permutations avoiding an arbitrary set of patterns (e.g. {udu,uuu}) and that conjectures (and who knows? even proves) exponential generating functions in the style of André's celebrated sec(x)+tan(x) .]

• John C. Miller's project about Number Theoretical sequences, Maple program.

• Matthew C. Russell' project about Somos-type sequences

• Yusra Naqvi is working on binomial coefficients for Macdonald polynomials
  [Not yet ready to be posted]

• Nathaniel Shar is creating a database of sequences related to linguistic extensions of Szemerédi's theorem
  [Not yet ready to be posted]

• Charles Wolf's project to explore systematically C-finite representations of sequences enumerating wide classes of forbidden patterns, with various alphabets.