{"docId":496,"paperId":496,"url":"https:\/\/dmtcs.episciences.org\/496","doi":"10.46298\/dmtcs.496","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":89,"name":"Vol. 12 no. 2"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-00990453","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-00990453v1","dateSubmitted":"2015-03-26 16:20:53","dateAccepted":"2015-06-09 14:47:35","datePublished":"2010-01-01 08:00:00","titles":{"en":"The absence of a pattern and the occurrences of another"},"authors":["B\u00f3na, Mikl\u00f3s"],"abstracts":{"en":"Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern q in permutations that avoid another given pattern r. In some cases, we find the pattern that occurs least often, (resp. most often) in all r-avoiding permutations. We also prove a few exact enumeration formulae, some of which are surprising."},"keywords":[["Permutation pattern"],["generating functions"],"[INFO.INFO-DM] Computer Science [cs]\/Discrete Mathematics [cs.DM]"]}