# Schedule for: 16w5048 - Workshop in Analytic and Probabilistic Combinatorics

Beginning on Sunday, October 23 and ending Friday October 28, 2016

All times in Banff, Alberta time, MDT (UTC-6).

Sunday, October 23
16:00 - 17:30 Check-in begins at 16:00 on Sunday and is open 24 hours (Front Desk - Professional Development Centre)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
20:00 - 22:00 Informal gathering (Corbett Hall Lounge (CH 2110))
Monday, October 24
07:00 - 09:15 Breakfast
Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
09:15 - 09:30 Introduction and Welcome by BIRS Station Manager (TCPL 201)
09:30 - 10:30 Helmut Prodinger: Forty years of tree enumeration (TCPL 201)
10:30 - 11:00 Coffee Break (TCPL Foyer)
11:00 - 11:30 Clemens Heuberger: Distribution of the Number of Factors in Monoids Generated by a Lucas sequence (TCPL 201)
11:30 - 13:00 Lunch (Vistas Dining Room)
13:00 - 14:00 Guided Tour of The Banff Centre
Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.
(Corbett Hall Lounge (CH 2110))
14:00 - 14:20 Group Photo
Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!
(TCPL Foyer)
14:30 - 15:00 Jay Pantone: Sorting with C-machines: Enumerative and Analytic Aspects (TCPL 201)
15:00 - 15:30 Coffee Break (TCPL Foyer)
15:30 - 16:00 Stephan Wagner: The Number of Automorphisms of Random Trees
By means of an asymptotic analysis of generating functions, we determine the limiting distribution of the order of the automorphism group of a random labeled tree. To be precise, we show that the logarithm of the number of automorphisms, suitably renormalized, converges weakly to a standard normal distribution. This result is also further extended to other random tree models.
(TCPL 201)
16:10 - 16:40 Cecilia Holmgren: Using Pólya urns to show normal limit laws for fringe subtrees in preferential attachment trees (TCPL 201)
16:50 - 17:20 Élie de Panafieu: Analytic combinatorics of graphs with marked subgraphs
We present a new proof of a result from Erdős and Rényi on the enumeration of graphs where a given subgraph is forbidden. It is based on generating function manipulations. Joint work in progress, with Gwendal Collet, Danièle Gardy, Bernhard Gittenberger and Vlady Ravelomanana.
(TCPL 201)
17:30 - 19:30 Dinner
A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.
(Vistas Dining Room)
Tuesday, October 25
07:00 - 09:15 Breakfast (Vistas Dining Room)
09:15 - 10:15 James Allen Fill: A local limit theorem for QuickSort key comparisons via multi-round smoothing (TCPL 201)
10:15 - 10:45 Coffee Break (TCPL Foyer)
10:45 - 11:15 Hsien-Kuei Hwang: Distribution of the coefficients of polynomials with only unit roots (TCPL 201)
11:30 - 13:30 Lunch (Vistas Dining Room)
13:30 - 14:00 Sara Kropf: Efficient Computation of Ratios of Stirling Numbers (TCPL 201)
14:10 - 14:40 Vincent Vatter: On the growth of grid classes and staircases of permutations (TCPL 201)
14:40 - 15:10 Coffee Break (TCPL Foyer)
15:10 - 15:40 Ronald Pavlov: Random subshifts of finite type: an introduction (TCPL 201)
15:50 - 16:20 Kevin McGoff: Random shifts of finite type: tools and techniques (TCPL 201)
16:30 - 17:30 Open Problem Session (TCPL 201)
17:30 - 19:30 Dinner (Vistas Dining Room)
Wednesday, October 26
07:00 - 09:15 Breakfast (Vistas Dining Room)
09:15 - 10:15 Marni Mishna: Universality classes for weighted lattice paths: where probability and ACSV meet
Lattice paths are very classic objects in both probability theory and enumerative combinatorics. In particular, weighted models bridge the gap between the two approaches very neatly. We consider an example, the Gouyou-Beauchamps model of lattice walks in the first quadrant, and discuss how to determine asymptotic enumeration formulas parameterized by the weights. The major tool is the theory of analytic combinatorics in several variables (ACSV) and we identify six different kinds of asymptotic regimes (called universality classes) which arise according to the values of the weights. Because we are able to explicitly and generically compute the constants of the asymptotic formula, we can determine a formula for a family of discrete harmonic functions. Furthermore, we are able to demonstrate an infinite class of models for which the counting generating function is not D-finite.
(TCPL 201)
10:15 - 10:45 Coffee Break (TCPL Foyer)
10:45 - 11:15 Jeff Gaither: Using Rooted Triplets to Identify Experimental Error in Cancer Data (TCPL 201)
11:25 - 11:55 Alejandro Morales: Asymptotics of the number of standard Young tableaux of skew shape
We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We compare our bounds with the existing bounds on the numbers of linear extensions. Joint work with Igor Pak and Greta Panova.
(TCPL 201)
11:55 - 13:30 Lunch (Vistas Dining Room)
13:30 - 17:30 Free Afternoon (Banff National Park)
17:30 - 19:30 Dinner (Vistas Dining Room)
Thursday, October 27
07:00 - 09:15 Breakfast (Vistas Dining Room)
09:15 - 10:15 Michael Drmota: Subgraph Counting in Series-Parallel Graphs and Infinite Dimensional Systems of Functional Equations (TCPL 201)
10:15 - 10:45 Coffee Break (TCPL Foyer)
10:45 - 11:15 David Galvin: Restricted Stirling and Lah numbers, and their inverses (TCPL 201)
11:30 - 13:30 Lunch (Vistas Dining Room)
13:30 - 14:00 Cécile Mailler: Measure-valued P\'olya urn processes (with Jean-François Marckert)
A P\'olya urn is a stochastic process that describes the composition of an urn that contains balls of different colours. The set of colours is usually a finite set $\{1, \ldots, d\}$. At each discrete-time step, one draws a ball uniformly at random in the urn (let $c$ be its colour), and replace it in the urn together with R_{c,i} balls of colour $i$, for all $1\leq i\leq d$ In this talk, I will present a generalisation of this model to an infinite, and potentially uncountable set of colours. In this new framework, the composition of the urn is a measure (possibly non-atomic) on a Polish space.
(TCPL 201)
14:10 - 14:40 Geronimo Uribe Bravo: Horizontal profiles of forests: scaling limits and time-change equations (TCPL 201)
14:40 - 15:10 Coffee Break (TCPL Foyer)
15:10 - 15:40 Daniel Panario: Periods of iterations of mappings over finite fields with restricted preimage sizes
Let $[n] = \{1, \dots, n\}$ and let $\Omega_n$ be the set of all mappings from $[n]$ to itself. Let $f$ be a random uniform element of $\Omega_n$ and let $\mathbf{T}(f)$ and $\mathbf{B}(f)$ denote, respectively, the least common multiple and the product of the length of the cycles of $f$. Harris proved in 1973 that $\log \mathbf{T}$ converges in distribution to a standard normal distribution and, in 2011, E. Schmutz obtained an asymptotic estimate on the logarithm of the expectation of $\mathbf{T}$ and $\mathbf{B}$ over all mappings on $n$ nodes. We obtain analogous results for random uniform mappings on $n = kr$ nodes with preimage sizes restricted to a set of the form $\{0,k\}$, where $k = k(r) \geq 2$. This is motivated by the use of these classes of mappings as heuristic models for the statistics of polynomials of the form $x^k + a$ over the integers modulo $p$, with $p \equiv 1 \pmod k$. We also exhibit and discuss our numerical results on this heuristic. Joint work with R. Martins, C. Qureshi and E. Schmutz.
(TCPL 201)
15:40 - 16:10 Pawel Hitczenko: On the game of Memory (TCPL 201)
17:30 - 19:30 Dinner (Vistas Dining Room)
Friday, October 28
07:00 - 09:00 Breakfast (Vistas Dining Room)
09:00 - 10:00 Informal discussions (TCPL 201)
10:00 - 10:30 Coffee Break (TCPL Foyer)
10:30 - 11:30 Informal discussions (TCPL 201)
11:30 - 12:00 Checkout by Noon
5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.
(Front Desk - Professional Development Centre)
12:00 - 13:30 Lunch from 11:30 to 13:30 (Vistas Dining Room)