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Abstract: The Four Colour Conjecture is reformulated as a statement about non-divisibility of certain binomial coefficients. This reformulation opens a (hypothetical) way of proving the Four Colour Theorem by taking advantage of recent progress in finding closed forms for binomial summations. 1 (Update)
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...establish Theorems 6 and 7. The details may be found in [2] The last reformulation, in terms of divisibility, is due to Matiyasevich [6]. THEOREM 8. There exist linear functions A k , B k , C k and D k (k = 1; 2; 986) of 21 variables such that the Four Color...
...establish Theorems 6 and 7. The details may be found in [2] The last reformulation, in terms of divisibility, is due to Matiyasevich [6]. Theorem 8. There exist linear functions A k , B k , C k , and D k (k =1,2, 986) of twenty one variables such that the Four Color...
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Temperley-Lieb Algebras And The Four-Color Theorem - Kauffman, Thomas (Correct)
Graph Planarity and Related Topics - Thomas (Correct)
An Update On The Four-Color Theorem - Thomas (1998) (Correct)
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0.6: Some Probabilistic Restatements of the Four Color Conjecture - Matiyasevich (2003) (Correct)
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9: Every planar map is four colorable (context) - Appel, Haken - 1977
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BibTeX entry: (Update)
Y. Matiyasevich, The Four Colour Theorem as a possible corollary of binomial summation, manuscript. http://citeseer.ist.psu.edu/matiyasevich98four.html More
@misc{ matiyasevich-four,
author = "Y. Matiyasevich",
title = "The Four Colour Theorem as a possible corollary of binomial summation",
text = "Y. Matiyasevich, The Four Colour Theorem as a possible corollary of binomial
summation, manuscript.",
url = "citeseer.ist.psu.edu/matiyasevich98four.html" }
Citations (may not include all citations):151 Every planar map is four colorable (context) - Appel, Haken - 1977
151 Every planar map is four colorable (context) - Appel, Haken et al. - 1977
151 Every planar map is four colorable (context) - Appel, Haken - 1989
69 An algorithmic proof theory for hypergeometric (context) - Wilf, Zeilberger - 1992
39 The Four-colour Theorem (context) - Robertson, Sanders et al.
36 Quickly excluding a planar graph (context) - Robertson, Seymour et al. - 1994
16 a new graph invariant and a criterion for planarity (context) - de Verdiere - 1993
10 Uber die Erganzungssatze zu den allgemeinen Reciprocit atsge.. (context) - Kummer
9 Thirteen colorful variations on Guthrie's four-color conject.. (context) - Saaty - 1972
8 An algebraic approach to the planar coloring problem (context) - Kauffman, Saleur - 1993
4 Is the four color theorem true (context) - Kainen - 1993
3 On edge-coloring graphs (context) - Hoffman, Mitchem et al. - 1992
2 The origin of the four-color conjecture (context) - May - 1965
2 Combinatorial recoupling theory and 3-manifold invariants (context) - Kauffman
2 AK Peters (context) - Petkovsek, Wilf et al. - 1996
2 topology and discrete physics (context) - Kauffman - 1994
1 with the collaboration of Gerda Fritsch (context) - Fritsch - 1994
1 Map coloring and the vector cross product (context) - Kaufmann - 1990
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