| viXra.org > Combinatorics and Graph Theory > 2411 |
 |
 |
| viXra.org > Combinatorics and Graph Theory > 2411 |
|
|
[4] viXra:2411.0100 [pdf] replaced on 2025-05-13 21:04:54
Authors: Volker W. Thürey
Comments: 4 Pages.
We introduce two constants. They are suitable for finite graphs. They can serve as ‘characteristic numbers’ or ‘dimensions’. Further, we define for each finite graph nine sequences. We will not calculate them.
Category: Combinatorics and Graph Theory
[3] viXra:2411.0065 [pdf] submitted on 2024-11-08 13:36:18
Authors: Peng Ji
Comments: 9 Pages.
Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. It is also a powerful tool for analysis. This article studies the symmetry of the coefficients in Formal Calculation. Three types of extended numbers were introduced, and many formulas for symmetric functions were obtained.
Category: Combinatorics and Graph Theory
[2] viXra:2411.0059 [pdf] submitted on 2024-11-07 00:45:23
Authors: John Clairmont
Comments: 133 Pages.
A heuristic algorithm is described for four col-oring planar graphs. The algorithm is based on theprinciple of breaking a problem into components andsolving them one at a time. The algorithm uses gen-eralized alternating chains of the most general kind,for instance they can have branches and self inter-sections. Alternating chains are found which, aftercompleting each major iteration of the algorithm, acertain property is preserved. This property ensuresthat a successive alternating chain will be easy tofind.Specifically the property ensures that the branchesof an alternating chain cannot conflict with each other,and a branch cannot conflict with itself. This algo-rithm solves one set of problems, but the solution hasit’s own set of problems. However I think these canbe easily resolved, leading to a new and simple proofof the Four Color Theorem.
Category: Combinatorics and Graph Theory
[1] viXra:2411.0054 [pdf] submitted on 2024-11-07 05:15:59
Authors: Peng Ji
Comments: 21 Pages.
Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained many results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry
Category: Combinatorics and Graph Theory
| Third-Party Links: |
|