Patterns in Combinatorics – PICS

In this project, we aim to develop and apply a new formalism to write
and study pattern correspondences between sets of combinatorial object
(permutations; words; trees; Dyck, Motzkin and other lattice paths),
the first steps of this formalism is already visible in our recently
published works. We plan to investigate pattern distributions,
pattern-aware bijective correspondences, asymptotic behavior of
patterns, and their connection to discrete structures from other
fields, such as DNA nullomers and RNA structures. We hope that our
explicit formalism will help to find new exciting results, especially
in cases where it is very difficult to study the original objects,
while their bijective images look more pleasant to work with.

A research group will be formed around the project coordinator, inside
the LIB (Laboratoire d'Informatique de Bourgogne, Dijon). We will
maintain existing international collaborations (Glasgow, Washington,
Florence, Bogotá) and seek for new interdisciplinary connections.
Artistic representation of patterns and participation in various
scientific popularization events are also included in our plans.