IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v386y2020ics0096300320304653.html
   My bibliography  Save this article

On algorithmic Coxeter spectral analysis of positive posets

Author

Listed:
  • Ga̧siorek, Marcin

Abstract

Following a general framework of Coxeter spectral analysis of signed graphs Δ and finite posets I introduced by Simson (SIAM J. Discrete Math. 27:827–854, 2013) we present efficient numerical algorithms for the Coxeter spectral study of finite posets I=({1,…,n},⪯I) that are positive in the sense that the symmetric Gram matrix GI:=12(CI+CItr)∈Mn(Q) is positive definite, where CI∈Mn(Z) is the incidence matrix of I encoding the relation ⪯I. In the framework of scientific computing we present a complete Coxeter spectral classification of finite positive posets I of size n=|I|<20. It extends one of the main results obtained in Ga̧siorek et al. (Eur. J. Comb. 48:127–142, 2015) for posets of size n ≤ 10. We also show that the connectivity of such posets I is determined by the complex Coxeter spectrum speccI⊆C; equivalently, by the Coxeter polynomial coxI(t)∈Z[t] od I.

Suggested Citation

  • Ga̧siorek, Marcin, 2020. "On algorithmic Coxeter spectral analysis of positive posets," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304653
    DOI: 10.1016/j.amc.2020.125507
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320304653
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125507?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel Simson & Katarzyna Zając, 2013. "A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-22, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304653. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.