ERROR

Vi är ledsna - även om vi gjorde vårt bästa: ett fel inträffade
Typedatabase
MessageYou have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near "AND SUBSTRING(categories_id,4,1) != "0") AS cat4, (SELECT categorie..." at line 5
QuerySELECT (SELECT categories_id FROM categories_description WHERE language_id = 17 AND categories_id = 000) AS cat1, (SELECT categories_id FROM categories_description WHERE language_id = 17 AND categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2, (SELECT categories_id FROM categories_description WHERE language_id = 17 AND categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3, (SELECT categories_id FROM categories_description WHERE language_id = 17 AND categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4, (SELECT categories_name FROM categories_description WHERE language_id = 17 AND categories_id = 000) AS cat1name, (SELECT categories_name FROM categories_description WHERE language_id = 17 AND categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2name, (SELECT categories_name FROM categories_description WHERE language_id = 17 AND categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3name, (SELECT categories_name FROM categories_description WHERE language_id = 17 AND categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4name, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = 000) AS cat1url, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2url, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3url, (SELECT url_text FROM commerce_seo_url_without_language WHERE categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4url, (SELECT wod_count_products FROM categories WHERE categories_id = 000) AS cat1cnt, (SELECT wod_count_products FROM categories WHERE categories_id = 00 AND SUBSTRING(categories_id,2,1) != "0") AS cat2cnt, (SELECT wod_count_products FROM categories WHERE categories_id = 0 AND SUBSTRING(categories_id,3,1) != "0") AS cat3cnt, (SELECT wod_count_products FROM categories WHERE categories_id = AND SUBSTRING(categories_id,4,1) != "0") AS cat4cnt

R. Balakrishnan & Xuding Zhu 
Combinatorial Nullstellensatz [EPUB ebook] 
With Applications to Graph Colouring

Support

Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to tackle combinatorial problems in diverse areas of mathematics. This book focuses on the applications of this theorem to graph colouring. A key step in the applications of Combinatorial Nullstellensatz is to show that the coefficient of a certain monomial in the expansion of a polynomial is nonzero. The major part of the book concentrates on three methods for calculating the coefficients:

  • Alon-Tarsi orientation: The task is to show that a graph has an orientation with given maximum out-degree and for which the number of even Eulerian sub-digraphs is different from the number of odd Eulerian sub-digraphs. In particular, this method is used to show that a graph whose edge set decomposes into a Hamilton cycle and vertex-disjoint triangles is 3-choosable, and that every planar graph has a matching whose deletion results in a 4-choosable graph.
  • Interpolation formula for the coefficient: This method is in particular used to show that toroidal grids of even order are 3-choosable, r-edge colourable r-regular planar graphs are r-edge choosable, and complete graphs of order p+1, where p is a prime, are p-edge choosable.
  • Coefficients as the permanents of matrices: This method is in particular used in the study of the list version of vertex-edge weighting and to show that every graph is (2, 3)-choosable.
  • It is suited as a reference book for a graduate course in mathematics.

    €25.62
    payment methods
    Buy this ebook and get 1 more FREE!
    Format EPUB ● Pages 150 ● ISBN 9781000426694 ● Publisher CRC Press ● Published 2021 ● Downloadable 3 times ● Currency EUR ● ID 7853273 ● Copy protection Adobe DRM
    Requires a DRM capable ebook reader

    More ebooks from the same author(s) / Editor

    49,921 Ebooks in this category