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Acknowledgement of priority - A fractional Helly theorem for boxes

Barany, I; Fodor, F; Martinez-Perez, A; Montejano, L; Oliveros, D; Por, A; (2018) Acknowledgement of priority - A fractional Helly theorem for boxes. [Editorial comment]. Computational Geometry: Theory and Applications , 67 (1) 10.1016/j.comgeo.2016.09.001. Green open access

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Abstract

In our recent paper [1] we prove a fractional Helly type theorem for boxes in Rd. This short note is to acknowledge priority: in 1980 Meir Katchalski [4] proved exactly the same result and in 1988 Jürgen Eckhoff [2] proved the same result in much more generality. In fact, Eckhoff established an upper bound theorem for the f -vectors of finite families of boxes in Rd from which his result is derived. Besides apologies for our ignorance we would like to mention that Eckhoff extended his results further in a more recent paper [3].

Type: Article
Title: Acknowledgement of priority - A fractional Helly theorem for boxes
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.comgeo.2016.09.001
Publisher version: http://doi.org/10.1016/j.comgeo.2016.09.001
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Fractional Helly theorems Intersection properties of boxes
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10042552
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