Multisets and a New Framework for Arithmetic - Data Structures Math Foundations
Explores multisets to redefine natural numbers, offering fresh insights into fundamental arithmetic operations and laws. Presents a simplified, logical approach to basic mathematics suitable for all levels.
Inclusion-Exclusion via Multisets - Data Structures in Mathematics Math Foundations
Explore inclusion/exclusion via multisets, expanding to integral multisets with negative multiplicities. Learn a conceptual approach to this fundamental Set Theory theorem and its applications.
An Introduction to the Tropical Calculus - Data Structures in Mathematics
Explore Tropical calculus, a novel approach to set algebra using unique addition and multiplication concepts derived from union and addition operations.
The Algebra of Natural Number Multisets - Data Structures in Mathematics
Explore multiset algebra in natural numbers, introducing notation and operations. Discover potential extensions to negative and rational multiplicities, with implications for modern algebra.
Multiset Arithmetic via Trees - Math Foundations 230
Explore multiset arithmetic using rooted trees, offering a visual representation for counting functions and new arithmetic operations. Gain insights into this alternative approach with concrete examples and useful notations.
Indexing and Iterating Design Space Permutations
Explore mathematical techniques for indexing and iterating design space permutations, focusing on perfect hash functions for efficient game state conversion and representation.