Special issue: Permutation Patterns 2019
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The *Permutation Patterns* conference series was initiated in 2003, with a first meeting organized by Michael Albert and Mike Atkinson at the university of Otago, New Zealand. At this first conference of the series, three days of talks were the occasion of sharing results and challenges about the enumeration of pattern-avoiding permutations, a research area which was gaining popularity at the time.
Twenty years after, some challenges were solved, others remain open, and more were discovered. One sure thing is that the conference has become wider, both in terms of topics and of number of attendees. Next to permutations, many other structures and their patterns are now discussed during our meetings (like lattice paths, set partitions, or tree, to name a few). In addition to enumerative combinatorics, other points of view attracted attention (like computationnal complexity, algebra, or probability theory). And the 2019 edition of the conference gathered 65 participants, from all over the world.
This volume follows the 2019 edition of the *Permutation patterns* conference, which was held in Zürich, during the week June 17-21, 2019. This 2019 meeting was preceded by a 3-day introductory workshop, primarily intended for students or researchers entering the research area. This meeting was a success, gathering 37 participants for four mini-courses by junior researchers.
The articles gathered in this volume are a sample of some topics currently of interest in the research on permutation patterns. Some of the results were presented during the conference, but not all.
The call for papers for this special volume of DMTCS closed on December 31st, 2019, just before Covid hit our world. The final articles were published only early 2023, and the pandemic is the main culprit which prevented us from putting this volume together faster. The additional article \[1\] should actually have been included in this volume, had we (editors) been faster in publishing it. This article has been fully refereed, but the author left academia before we asked him to provide a revision accommodating minor changes.
We thank all authors who contributed their work to this volume, the referees for their expert opinion and constructive feedback, and Jens Gustedt for his support as DMTCS editor-in-chief. We are also grateful to the Permutation Patterns community in general, for making our yearly meetings a friendly place to learn new results and have scientific exchanges in a relaxed atmosphere. After two years of virtual meeting in 2020 and 2021, we have all been very grateful to meet again in person at the Valparaiso meeting in 2022, and look forward to the 20th anniversary of the conference in 2023 in Dijon!
**Miklós Bóna**, University of Florida — Gainesville, USA
**Mathilde Bouvel**, Loria, CNRS and Univ. Lorraine, France
**Lara Pudwell**, Valparaiso University, USA
**Vincent Vatter**, University of Florida — Gainesville, USA
**Reference**
\[1\] Sam Miner, Enumeration of several two-by-four classes, Arxiv preprint 1610.01908, <https://arxiv.org/abs/1610.01908v1>.
, Hadas Shachnai, Alexander Wolff