Metroplex Algebraic Geometry, Algebra and Number
Theory (AGANT) Seminar,
a joint venture of
Date/Time/Room: Wednesday (03/18/2015) at
2:10 pm in 113 Pickard Hall
Phillipson, Department of
Mathematics, Texas A&M
"Fillings of Layer
Abstract: In a permutation matrix,
occurrences of northeast (ne) and southeast (se) 2-chains
correspond to inversions and co-inversions, respectfully. If
permutations are instead represented by fillings of two Ferrers
diagrams, then the sum of these chains in each diagram corresponds
to crossing (cros) and nestings (nest) in the permutation. In
2005, Sylvie Corteel proved that the distribution of the joint
statistic (cros,nest) is symmetric in permutations. In this talk,
we'll discuss these results and introduce layer polyominoes, which
are row convex and intersection-free. Fillings of layer
polyominoes generalize inversions/co-inversions and
crossings/nestings to chains allowing us to see relations with
other patterns and structures. We will conclude with two simple
bijections extending the symmetry of the joint statistic (ne,se).
An interactive map of UTA may be found
which gives both buildings and parking lots (use the menu
on the left of the map). Note that PKH is Pickard Hall and is on
South Nedderman Drive. S. West St is one-way northbound between W.
Mitchell St and 3rd St. Parking is available in the nearby (East
and SE of PKH) parking lots with a UTA permit (but many people
park there late on Fridays with no permit and are not caught,
though there are counterexamples to this statement!). There are a
few metered parking spots on the East side of Pickard Hall on S.
West St. Visitor (free), & metered, parking is available by
Davis Hall (marked DH in SW part of the submap). A parking garage
(expensive) is nextdoor to PKH (use West St to get to it).
Note that if heading south on Cooper, then no left
turn is allowed to Nedderman Dr. Recommended route from UNT:
eventually head south on Hwy 360 (or Industrial Blvd = Collins),
West on Abram, south (left) on Center, West (right) on W Mitchell.
Then use map. Alternatively, using a west route, get to I30
heading East, & follow directions from TCU given below. From
TCU: east on I30, exit Cooper, South on Cooper, left (East) on W.
Mitchell, then use map.
The closest door to PKH 113 is located at the corner
of S. Nedderman Dr and S. West St.
etc on arrangements/directions should be sent to Dr
Vancliff; if travelling from out of town, notify Dr Vancliff,
as we will delay starting the talk for you if you are a little