Résumé : Permutations, words, tableaux, and other such families of objects often play a role in diverse subfields of mathematics, physics and computer science. When the structure of the object under investigation is known there are well-established tools, such as symbolic and analytic combinatorics, that derive an enumeration, asymptotics, and the ability to randomly generate instances of the objects. However, the initial step from a definition of the object to a structural description is often ad-hoc, human-staring-at-a-blackboard type of work. We thus tried to automatize this work via an implementation "Combinatorial Exploration" in Python and applied it to several combinatorial objects, such as permutations, set partitions and words. In this talk we will focus on permutations and show how we have found structural descriptions of so-called 'permutation classes'. (See the project webpage: https://permutatriangle.github.io/papers/2019-02-27-combex.html)

 [Slides.pdf] [arXiv]

Dernière modification : Thursday 21 November 2024

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