Sidorenko conjectured an integral inequality for a product of functions h(xi, yi) where the diagram of the product is a bipartite graph G in [8]. We answered the conjecture positively when the function h is multiplicative or additive separable with respect to variables x and y.
| Published in | Mathematics Letters (Volume 1, Issue 3) |
| DOI | 10.11648/j.ml.20150103.11 |
| Page(s) | 17-19 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Sidorenko’s Conjecture, Bipartite Graph, Lebesgue Measure, Measurable Function
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| [2] | Sidorenko, A. F, Inequalities for functional generated by bipartite graphs (in Russian), Discrete Mathematics and Applications 3 (3) 50-65 (1991). |
| [3] | Sidorenko, A. F., Exremal problems in graph theory and inequalities in functional analysis (in Russian). In Lupanov, O. B, ed., Proceedings of the Soviet Seminar on Discrete Mathematics and it Applications (in Russian), pp. 99-105. Moscow: Moscow State University 1986, MR88m: 05053. |
| [4] | Mulholland, H. P., Smith, C. A. B., An inequality arising in genetical theory, Amer. Math. Mon. 66, 673-683 (1959). |
| [5] | Blakley, G. R, Roy, P., Hölder type inequality for symmetrical matrices with nonnegative entries. Proc. Am. Math. Soc. 16, 1244-1245 (1965). |
| [6] | Atkinson, F. V., Watterson, G. A., Moran, P. A. D., A matrix inequality. Q. J. Math. Oxf. II Ser. 11, 137-140 (1960). |
| [7] | London, D., Two equalities in nonnegative symmetric matrices. Pac. J. Math.16, 515-536(1966). |
| [8] | Sidorenko, A., A Correlation Inequality for Bipartite Graphs., Graphs and Combinatorics (1993) 9, 201-204. |
APA Style
Danyal Soybas, Onur Alp Ilhan. (2016). A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs. Mathematics Letters, 1(3), 17-19. https://doi.org/10.11648/j.ml.20150103.11
ACS Style
Danyal Soybas; Onur Alp Ilhan. A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs. Math. Lett. 2016, 1(3), 17-19. doi: 10.11648/j.ml.20150103.11
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Download@article{10.11648/j.ml.20150103.11,
author = {Danyal Soybas and Onur Alp Ilhan},
title = {A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs},
journal = {Mathematics Letters},
volume = {1},
number = {3},
pages = {17-19},
doi = {10.11648/j.ml.20150103.11},
url = {https://doi.org/10.11648/j.ml.20150103.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20150103.11},
abstract = {Sidorenko conjectured an integral inequality for a product of functions h(xi, yi) where the diagram of the product is a bipartite graph G in [8]. We answered the conjecture positively when the function h is multiplicative or additive separable with respect to variables x and y.},
year = {2016}
}
TY - JOUR T1 - A Partial Answer to Sidorenko’s Conjecture on a Correlation Inequality for Bipartite Graphs AU - Danyal Soybas AU - Onur Alp Ilhan Y1 - 2016/01/05 PY - 2016 N1 - https://doi.org/10.11648/j.ml.20150103.11 DO - 10.11648/j.ml.20150103.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 17 EP - 19 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20150103.11 AB - Sidorenko conjectured an integral inequality for a product of functions h(xi, yi) where the diagram of the product is a bipartite graph G in [8]. We answered the conjecture positively when the function h is multiplicative or additive separable with respect to variables x and y. VL - 1 IS - 3 ER -
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