On the representability of the biuniform matroid

Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems i...

Full description

Saved in:
Bibliographic Details
Main Authors: Ball, Simeon, Padró, Carles, Weiner, Zsuzsa, Xing, Chaoping
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2014
Subjects:
Online Access:https://hdl.handle.net/10356/101419
http://hdl.handle.net/10220/18666
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-101419
record_format dspace
spelling sg-ntu-dr.10356-1014192023-02-28T19:41:32Z On the representability of the biuniform matroid Ball, Simeon Padró, Carles Weiner, Zsuzsa Xing, Chaoping School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields. Published version 2014-01-22T01:53:55Z 2019-12-06T20:38:27Z 2014-01-22T01:53:55Z 2019-12-06T20:38:27Z 2013 2013 Journal Article Ball, S., Padró, C., Weiner, Z., & Xing, C. (2013). On the representability of the biuniform matroid. SIAM journal on discrete mathematics, 27(3), 1482-1491. https://hdl.handle.net/10356/101419 http://hdl.handle.net/10220/18666 10.1137/120886960 en SIAM journal on discrete mathematics © 2013 Society for Industrial and Applied Mathematics (SIAM). This paper was published in SIAM Journal on Discrete Mathematics and is made available as an electronic reprint (preprint) with permission of SIAM. The paper can be found at the following official DOI: [http://dx.doi.org/10.1137/120886960]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Discrete mathematics
spellingShingle DRNTU::Science::Mathematics::Discrete mathematics
Ball, Simeon
Padró, Carles
Weiner, Zsuzsa
Xing, Chaoping
On the representability of the biuniform matroid
description Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Ball, Simeon
Padró, Carles
Weiner, Zsuzsa
Xing, Chaoping
format Article
author Ball, Simeon
Padró, Carles
Weiner, Zsuzsa
Xing, Chaoping
author_sort Ball, Simeon
title On the representability of the biuniform matroid
title_short On the representability of the biuniform matroid
title_full On the representability of the biuniform matroid
title_fullStr On the representability of the biuniform matroid
title_full_unstemmed On the representability of the biuniform matroid
title_sort on the representability of the biuniform matroid
publishDate 2014
url https://hdl.handle.net/10356/101419
http://hdl.handle.net/10220/18666
_version_ 1759854057271328768