Symmetric Boolean Algebras
Rafael Diaz, Mariolys Rivas

TL;DR
This paper introduces Boolean algebras within a linear framework, explores their symmetric powers, and provides explicit formulas and symmetric inclusion-exclusion principles, advancing the algebraic understanding of these structures.
Contribution
It defines Boolean algebras in a linear setting, derives explicit product formulas for symmetric powers, and formulates symmetric inclusion-exclusion principles, offering new algebraic tools.
Findings
Explicit formulas for products in symmetric Boolean algebras
Symmetric forms of the inclusion-exclusion principle
Enhanced algebraic understanding of linear Boolean structures
Abstract
We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
