Decomposing labeled interval orders as pairs of permutations

Claesson, Anders and Hannah, Stuart A. (2014) Decomposing labeled interval orders as pairs of permutations. The Electronic Journal of Combinatorics, 21 (4). P4.16. ISSN 1077-8926 (https://doi.org/10.37236/4360)

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Abstract

We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices fixed under this involution are in bijection with labeled interval orders and that they decompose to a pair consisting of a permutation and an inversion table. To fully classify such pairs, results pertaining to the enumeration of permutations having a given set of ascent bottoms are given. This allows for a new formula for the number of labeled interval orders.

ORCID iDs

Claesson, Anders ORCID logoORCID: https://orcid.org/0000-0001-5797-8673 and Hannah, Stuart A.;
  • Item type:Article
    ID code:53749
    Dates:
    Date
    Event
    16 October 2014
    Published
    8 October 2014
    Accepted
    Keywords:ballot matrix, composition matrix, sign reversing involution, interval order, 2+2-free posset, ascent bottom, Mathematics, Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science
    Subjects:Science > Mathematics
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:14 Jul 2015 08:52
    Last modified:10 May 2022 00:18
    URI:https://strathprints.strath.ac.uk/id/eprint/53749
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