Counting segmented permutations using bicoloured Dyck paths
Claesson, Anders (2005) Counting segmented permutations using bicoloured Dyck paths. The Electronic Journal of Combinatorics, 12. R39. ISSN 10778926
Full text not available in this repository.Request a copyAbstract
A bicoloured Dyck path is a Dyck path in which each upstep is assigned one of two colours, say, red and green. We say that a permutation π is σsegmented if every occurrence o of σ in π is a segmentoccurrence (i.e., o is a contiguous subword in π). We show combinatorially the following two results: The 132segmented permutations of length n with k occurrences of 132 are in onetoone correspondence with bicoloured Dyck paths of length 2n−4k with k red upsteps. Similarly, the 123segmented permutations of length n with k occurrences of 123 are in onetoone correspondence with bicoloured Dyck paths of length 2n−4k with k red upsteps, each of height less than 2. We enumerate the permutations above by enumerating the corresponding bicoloured Dyck paths. More generally, we present a bivariate generating function for the number of bicoloured Dyck paths of length 2n with k red upsteps, each of height less than h. This generating function is expressed in terms of Chebyshev polynomials of the second kind.
ORCID iDs
Claesson, Anders ORCID: https://orcid.org/0000000157978673;

Item type: Article ID code: 49794 Dates: DateEvent17 August 2005PublishedKeywords: bicoloured Dyck path, Dyck path, segmented permutations, Electronic computers. Computer science, Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science Subjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 14 Oct 2014 13:49 Last modified: 03 Dec 2022 03:45 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/49794