Séminaire Lotharingien de Combinatoire, B88pref (2022), 1 p.

Christian Krattenthaler


The 88th Meeting of the Séminaire Lotharingien de Combinatoire took place from September 4 to 7, 2022, in the Bundesinstitut für Erwachsenenbildung in Strobl (Austria).

The main lectures were given by Philippe Biane (Marne-la-Vallée) and Einar Steingrímsson (Strathclyde). In his first two lectures, Biane presented us a beautiful survey (Lecture 1, Lecture 2) of cummulants - classical, free, and Boolean - and their identities, and a brief summary of their applications. His third lecture was devoted to Laver tables; fascinating tables of numbers which - strangely enough - have their origin in the theory of very large cardinals. Steingrímsson's lectures on the other hand were concerned with the question of which sequences arise as moments of positive measures on the reals. In the centre of these lectures was a striking result on the enumeration of permutations with 14 different statistics and the related continued fraction.

The contributed talks (see the detailed list below) covered a variety of different topics, including conjectures and questions on cumulants, partition theory, Tamari lattices, polytopes and subword complexes, gentle algebras, and symmetric functions. Obviously, Wadim Zudilin won the contest of the most original title.

The weather was again fantastic. Obviously, the lunch breaks were intensively used for swimming in the Wolfgangsee, and for hikes and excursions in the area. It was great to experience a real (= non-Zoom) meeting, with the opportunity to have spontaneous questions during talks, to have discussions in various formations and formats, and simply to talk to each other!

Contributed talks:

Houcine BEN DALI: The integrality in the Matching-Jack Conjecture

Noémie CARTIER: Lattice quotients of weak order intervals in subword complexes

Cesar CEBALLOS: Reconstruction of polytopes and Kalai's conjecture on reconstruction of spheres

Clément CHENEVIÈRE: Linear intervals in the Tamari and the Dyck lattices

Benjamin DEQUÊNE: A generalization of perfectly clustering words through brick band modules of certain gentle algebras

Christian KRATTENTHALER: Proofs of Borwein conjectures

Franz LEHNER: Some questions on cumulants

Florian SCHREIER-AIGNER: A family of equivariant bijections between noncrossing and nonnesting matchings of type A

Nicholas SMOOT: Partitions, kernels, and the localization method

Ali Kemal UNCU: Sequences in overpartitions

Wadim ZUDILIN: q-rious !-ratios

List of Partipants: