<div class="csl-bib-body">
<div class="csl-entry">Bergold, H., Egeling, L., & Hoang, H. P. (2025). Signotopes with Few Plus Signs. In O. Aichholzer & H. Wang (Eds.), <i>41st International Symposium on Computational Geometry (SoCG 2025)</i>. Schloss Dagstuhl. https://doi.org/10.4230/LIPIcs.SoCG.2025.16</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/221520
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dc.description.abstract
Arrangements of pseudohyperplanes are widely studied in computational geometry. A rich subclass of pseudohyerplane arrangements, which has gained more attention in recent years, is the so-called signotopes. Introduced by Manin and Schechtman (1989), the higher Bruhat order is a natural order of r-signotopes on n elements, with the signotope corresponding to the cyclic arrangement as the minimal element. In this paper, we show that the lower (and by symmetry upper) levels of this higher Bruhat order contain the same number of elements for a fixed difference n - r. This result implies that given the difference d = n - r and p, the number of one-element extensions of the cyclic arrangement of n hyperplanes in Rd with at most p points on one side of the extending pseudohyperplane does not depend on n, as long as n ≥ d + p.
en
dc.language.iso
en
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dc.relation.ispartofseries
Leibniz International Proceedings in Informatics (LIPIcs)
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dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
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dc.subject
counting
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dc.subject
Ferrers diagram
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dc.subject
flip graph
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dc.subject
higher Bruhat order
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dc.subject
one-element extension
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dc.subject
signotope
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dc.title
Signotopes with Few Plus Signs
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dc.type
Inproceedings
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dc.type
Konferenzbeitrag
de
dc.rights.license
Creative Commons Attribution 4.0 International
en
dc.rights.license
Creative Commons Namensnennung 4.0 International
de
dc.contributor.affiliation
Freie Universität Berlin, Germany
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dc.contributor.affiliation
ETH Zurich, Switzerland
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dc.contributor.editoraffiliation
Graz University of Technology, Austria
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dc.contributor.editoraffiliation
University of Utah, United States of America (the)