Sectoral Structures Theory

Sectoral Structures Theory is a novel, interdisciplinary mathematical framework which studies the continuous arrangements of circular sectors into sectoral structures. This work explores enumerative functions of structural sets, their connections to Losanitsch’s triangle, and their links to arithmetic functions. We establish the foundations of the theory within geometric combinatorics, graph theory, and number theory. After that, we use matrices and polynomials to describe and analyze sectoral structures. We integrate concepts from algebraic topology and algebraic geometry to study mappings and operations on these structures. The same concepts are expanded to define and study sectoral substructures and superstructures. Concepts from circle packings are used to investigate the covers and compliments as well. We utilize group theory to study various types of symmetries of sectoral sequences. The book concludes with an analysis of string embeddings into sectoral structures.