Mathematisches Forschungsinstitut Oberwolfach Report No

Enumerative Combinatorics focusses on the exact and asymptotic counting of combinatorial objects. It is strongly connected to the probabilistic analysis of large combinatorial structures and has fruitful connections to several disciplines, including statistical physics, algebraic combinatorics, graph theory and computer science. This workshop brought together experts from all these various fields, including also computer algebra, with the goal of promoting cooperation and interaction among researchers with largely varying backgrounds. Mathematics Subject Classification (2010): Primary: 05A; Secondary: 05E, 05C80, 05E, 60C05, 60J, 68R, 82B. Introduction by the Organisers The workshop Enumerative Combinatorics organized by Mireille Bousquet-Mélou (Bordeaux), Michael Drmota (Vienna), Christian Krattenthaler (Vienna), and Marc Noy (Barcelona) took place on March 2-8, 2014. There were over 50 participants from the US, Canada, Australia, Japan, Korea, and various European countries. The program consisted of 13 one hour lectures, accompanied by 17 shorter contributions and the special session of 5 presentations by Oberwolfach Leibniz graduate students. There was also a lively problem session led by Svante Linusson. The lectures were intended to provide overviews of the state of the art in various areas and to present relevant new results. The lectures and short talks ranged over a wide variety of topics including classical enumerative problems, algebraic combinatorics, asymptotic and probabilistic methods, statistical 2 Oberwolfach Report 12/2014 physics, methods from computer algebra, among others. Special attention was paid throughout to providing a platform for younger researchers to present themselves and their results. This report contains extended abstracts of the talks and the statements of the problems that were posed during the problem session. This was the first workshop held on Enumerative Combinatorics. The goal of the workshop was to bring together researchers from different fields with a common interest in enumeration, whether from an algebraic, analytic, probabilistic, geometric or computational angle, in order to enhance collaboration and new research projects. The organizers believe this goal was amply achieved, as demonstrated by the strong interaction among the participants and the lively discussions in and outside the lecture room during the whole week. On behalf of all participants, the organizers would like to thank the staff and the director of the Mathematisches Forschungsinstitut Oberwolfach for providing such a stimulating and inspiring atmosphere. Enumerative Combinatorics 3 Workshop: Enumerative Combinatorics