Combinatorics and Graph Theory

2401 Submissions

[2] viXra:2401.0137 [pdf] submitted on 2024-01-29 04:31:14

Tessellations and Sweeping Nets: Advancing the Calculus of Geometric Logic

Authors: Parker Emmerson
Comments: 44 Pages. Note by viXra Admin: Please list author name in the order of fist name followed by ;ast name!)

In this paper, we have explained how logic-vectors can be interpreted as a geometrical representation over computational engines and how it can be implemented in code using large language models. We have also proposed the usage of Time Compass to derive logic-vector evolution over a quasi-chaotic system and its direct manipulation on the tessellation Colormap. This paper focuses on the optimal arrangement of reflecting points for efficient ray tracing given limited sweep time. We examine spatial configurations, employing our core concept of a sweeping subnet and defining a causal barrier to capture constraints imposed by time.We will also discuss the influence of these constructions on the design of an algorithm for approximating optimal tessellations.I have provided code for each of the graphs, as the mathematics is demonstrated unequivocally by their implementation. The reader can test out the reality of this system by visualizing the graphs themselves using Python in a suitable environment like Google Colaboratory.
Category: Combinatorics and Graph Theory

[1] viXra:2401.0100 [pdf] replaced on 2026-01-22 00:20:04

Dimensions of a Graph

Authors: Volker W. Thürey
Comments: 6 Pages.

We introduce eight infinite sets of constants.Some we calculate. Roughly speaking, we seek graphs as small as possible. The graphs serve as examples for different kinds of `dimensions'. In the second part `Points', we place points on the plane, and from this, we ask infinite many questions. In a third part, we introduce for each graph a sequence called the 'Thuerey Numbers'.At the end, we summarize the open questions.
Category: Combinatorics and Graph Theory