Colloquium: Ruth Davidson

Event Type: 
Ruth Davidson
Event Date: 
Thursday, January 14, 2016 -
3:30pm to 5:00pm
SMLC 356
General PublicFaculty/StaffStudentsAlumni/Friends
Stat Group

Event Description: 

Title: A new shellability proof of an old identity of Dixon
Abstract:  We give a new proof of an old identity of Dixon (1865-1936) that
uses tools from topological combinatorics.  Dixon's identity is
re-established by constructing an infinite family of non-pure simplicial
complexes $\Delta(n)$, indexed by the positive integers, such that the
alternating sum of the numbers of faces of $\Delta(n)$ of each dimension is
the left-hand side of the the identity.  We show that $\Delta(n)$ is
shellable for all $n$. Then, using the fact that a shellable simplicial
complex is homotopy equivalent to a wedge of spheres, we compute the Betti
numbers of $\Delta(n)$ by counting (via a generating function) the number
of facets of $\Delta(n)$ of each dimension that attach along their entire
boundary in the shelling order. In other words, Dixon's identity is
re-established by using the Euler-Poincar\'{e} relation. No background in
topological combinatorics will be assumed for this talk.  This is joint
work with Augustine O'Keefe and Daniel Parry.

Event Contact

Contact Name: Yan Lu

Contact Phone: 505-277-2544

Contact Email: