Vít Jelínek - Counting self-dual interval orders

dmtcs:2932 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2932
Counting self-dual interval orders

Authors: Vít Jelínek ORCID-iD

    In this paper, we first derive an explicit formula for the generating function that counts unlabeled interval orders (a.k.a. (2+2)-free posets) with respect to several natural statistics, including their size, magnitude, and the number of minimal and maximal elements. In the second part of the paper, we derive a generating function for the number of self-dual unlabeled interval orders, with respect to the same statistics. Our method is based on a bijective correspondence between interval orders and upper-triangular matrices in which each row and column has a positive entry.


    Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
    Section: Proceedings
    Published on: January 1, 2011
    Imported on: January 31, 2017
    Keywords: interval orders,(\textrm2+2)-free posets,self-dual posets,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Klassische Kombinatorik und Anwendungen; Funder: Austrian Science Fund (FWF); Code: Z 130

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    Source : ScholeXplorer IsVersionOf DOI 10.1016/j.jcta.2011.11.010
    • 10.1016/j.jcta.2011.11.010
    Counting general and self-dual interval orders
    Jelínek, Vít ;

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