IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789812704276_0014.html
   My bibliography  Save this book chapter

Lecture 2 Residue Formulae For Volumes And Number Of Integral Points In Convex Rational Polytopes

In: European Women In Mathematics

Author

Listed:
  • MICHÈLE VERGNE

    (Centre de Mathematiques, Ecole Polytechnique, F-91128 Palaiseau Cedex, France)

Abstract

We first discuss here some classical results on the number of points with integral coordinates in convex rational polytopes P ⊂ Rn starting with Ehrhart's theorem. Then, following Baldoni-Vergne and Szenes-Vergne, we present some recent results giving number of points with integral coordinates in P in terms of multidimensional residues. In particular, this allows to recover relations established by Khovanskii-Pukhlikov, Cappell-Shaneson and Brion-Vergne between volumes and number of points with integral coordinates in families of polytopes with parallel facets.

Suggested Citation

  • Michèle Vergne, 2003. "Lecture 2 Residue Formulae For Volumes And Number Of Integral Points In Convex Rational Polytopes," World Scientific Book Chapters, in: Emilia Mezzetti & Sylvie Paycha (ed.), European Women In Mathematics, chapter 14, pages 245-285, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812704276_0014
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/pdf/10.1142/9789812704276_0014
    Download Restriction: Ebook Access is available upon purchase.

    File URL: https://www.worldscientific.com/doi/abs/10.1142/9789812704276_0014
    Download Restriction: Ebook Access is available upon purchase.
    ---><---

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

    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:wsi:wschap:9789812704276_0014. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/page/worldscibooks .

    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.