Vienna, Austria
September 6-9, 2016

Program

Preliminary timetable

	Tuesday	Wednesday	Thursday	Friday
9:00-10:00	Course 1-1 Cécile Mailler	Course 2-1 Élie de Panafieu	Course 3-1 Rika Yatchak	Course 1-3 Cécile Mailler
10:00-10:30	Coffee break	Coffee break	Coffee break	Coffee break
10:30-11:30	Course 1-2 Cécile Mailler	Course 2-2 Élie de Panafieu	Course 3-2 Rika Yatchak	Course 2-3 Élie de Panafieu
11:30-12:30	Long talk 1 Tomack Gilmore	Long talk 2 Robin Sulzgruber	Open Problems 3	Course 3-3 Rika Yatchak
12:30-14:00	Lunch break	Lunch break	Lunch break
14:00-15:00	Short talks 1 Emma Yu Jin Maciej Bendkowski	Short talks 2 Manjil Saikia Dorottya Beringer	Short talks 3 Matthieu Dien Martin Zeiner
15:00-16:00	Course 1-Exercises	Course 2-Exercises	Course 3-Exercises
16:00-16:30	Coffee break	Coffee break	Coffee break
16:30-18:00	Open problems 1	Open problems 2	Open problems 4

Abstracts

Tomack Gilmore

Holey matrimony: marrying two approaches to the dimer problem

In this talk I will discuss two different methods for counting dimer coverings on the hexagonal lattice and show how these may be combined in order to enumerate rhombus tilings of hexagons that contain holes (also known as holey hexagons).

Robin Sulzgruber

The complexity of the Novelli-Pak-Stoyanovskii algorithm

The Novelli-Pak-Stoyanovskii algorithm is a sorting algorithm for Young tableaux that was originally devised to give a direct bijective proof of the celebrated hook-length formula for the number of standard Young tableaux of a given shape. I will recall this algorithm and present some new results on its average and worst case complexity, some bijective and some asymptotic in nature. I will also give a crash course on making an educated guess.

Emma Yu Jin

Open Problems on Hook formulas for skew shapes

The classical Hook-length formula for the number of Standard Young tableaux was discovered by Frame, Robinson and Thrall in 1954.\\ By now it has numerous proofs: probabilistic, bijective, analytic, geometric, etc. In 2014, Naruse remarkably found a Hook-length formula for the number of skew Young tableaux and in 2015, Morales-Pak-Panova provided an algebraic and a combinatorial proof of Narase's formula. In this talk I will present Morales-Pak-Panova's results and their open problems on the hook-length formula for skew shapes.

Maciej Bendkowski

Quantitative aspects of normal-order reduction in combinatory logic

We present a quantitative basis-independent analysis of combinatory logic. Using a general argument regarding plane binary trees with labelled leaves, we generalise the results of David et al. and Bendkowski et al. to all Turing-complete combinator bases proving, inter alia, that asymptotically almost no combinator is strongly normalising nor typeable. We exploit the structure of recently discovered normal-order reduction grammars showing that for each positive n, the set of SK-combinators reducing in n normal-order reduction steps has positive asymptotic density in the set of all combinators. Our approach is constructive, allowing us to systematically find new asymptotically significant fractions of normalising combinators. We show that the density of normalising combinators cannot be less than 34%, improving the previously best lower bound of approximately 3%. Finally, we present some super-computer experimental results, conjecturing that the density of normalising combinators is close to 85%.

Matthieu Dien

On the combinatorics of concurrent programs

In this talk, I will propose to take a combinatorial point of view of what is a concurrent process. Then I will present some combinatorial models of concurrent processes, using the symbolic method, and show some results obtained by analytic combinatorics methods. To conclude, I will introduce an original operator (for the symbolic method) and present some use cases.

Manjil Saikia

Graphical Condensation and Counting Perfect Matchings of Planar Graphs

The method of graphical condensation was devised by Eric Kuo to compute the number of perfect matchings of planar bipartite graphs. This was subsequently generalized by Mihai Ciucu for planar graphs. We briefly survey these results and present our common generalization of both Kuo and Ciucu's results. If time permits, we shall present few applications of the result in computing tilings of some combinatorial regions.

Martin Zeiner

Broadcasting in random trees

Dorottya Beringer

On percolation critical probabilities and unimodular random graphs

There are several definitions of percolation critical probability, which have turned out to be equivalent for transitive graphs. We investigate the relationship between these different definitions when the graph is an ergodic unimodular random graph, which is the natural extension of transitivity to the disordered setting. We give certain conditions, which imply the equality of the critical probabilities, and we show by examples, that some of the critical probabilities can be distinct.