Partial Orders, Maxels, and Möbius Functions in Posets

Explore advanced concepts in Boolean algebra and circuit analysis in this 34-minute lecture. Delve into the Boole-Mobius transform, connecting Boolean functions and Boole polynumbers. Examine partial orders, maxels, and Mobius functions on partially ordered sets (posets). Learn about the inverse of the Boole-Mobius transform through matrix inversion and the modern theory of maxels. Discover a novel bar notation for negative numbers, revolutionizing fundamental arithmetic notation. Gain insights into the Incidence Algebra of a poset and its applications in electrical engineering. Cover topics including linear orders, partial orders on natural numbers, divisibility relations, and maxel algebra of posets.

Introduction
Linear orders
Partial orders on Nat
Divisibility relation on 1,2,3...
Converting to a partial order
Maxel algebra of a poset
Inverses in MaxP