The odd case of Rota's bases conjecture
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10312934" target="_blank" >RIV/00216208:11320/15:10312934 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2015.06.015" target="_blank" >http://dx.doi.org/10.1016/j.aim.2015.06.015</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2015.06.015" target="_blank" >10.1016/j.aim.2015.06.015</a>
Alternative languages
Result language
angličtina
Original language name
The odd case of Rota's bases conjecture
Original language description
The paper links four conjectures: (1) (Rota's bases conjecture): For any system A = ((1)A, . . . , (n)A) of non-singular real valued matrices the multiset of all columns of matrices in A can be decomposed into n independent systems of representatives ofA. (2) (Alon-Tarsi): For even n, the number of even n x n Latin squares differs from the number of odd n x n Latin squares. (3) (Stones-Wanless, Kotler): For all n, the number of even n x n Latin squares with the identity permutation as first row and first column differs from the number of odd n x n Latin squares of this type. (4) (Aharoni-Berger): Let M and N be two matroids on the same vertex set, and let A(1), . . . , A(n) be sets of size n+1 belonging to the intersection of M and N. Then there exists a set belonging to the intersection of M and N meeting all A(i). Huang and Rota [8] and independently Onn [11] proved that for any n (2) implies (1). We prove equivalence between (2) and (3). Using this, and a special case of (4), we pr
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Mathematics
ISSN
0001-8708
e-ISSN
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Volume of the periodical
282
Issue of the periodical within the volume
July
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
427-442
UT code for WoS article
000359682800012
EID of the result in the Scopus database
2-s2.0-84937828090