Fisher's Inequality: Linear Algebraic Proof Techniques for Combinatorics


Title: Fisher's Inequality: Linear Algebraic Proof Techniques for Combinatorics
Authors: Chelsea Edmonds and Lawrence C. Paulson
Submission date: 2022-04-21
Abstract: Linear algebraic techniques are powerful, yet often underrated tools in combinatorial proofs. This formalisation provides a library including matrix representations of incidence set systems, general formal proof techniques for the rank argument and linear bound argument, and finally a formalisation of a number of variations of the well-known Fisher's inequality. We build on our prior work formalising combinatorial design theory using a locale-centric approach, including extensions such as constant intersect designs and dual incidence systems. In addition to Fisher's inequality, we also formalise proofs on other incidence system properties using the incidence matrix representation, such as design existence, dual system relationships and incidence system isomorphisms. This formalisation is presented in the paper "Formalising Fisher's Inequality: Formal Linear Algebraic Techniques in Combinatorics", accepted to ITP 2022.
  author  = {Chelsea Edmonds and Lawrence C. Paulson},
  title   = {Fisher's Inequality: Linear Algebraic Proof Techniques for Combinatorics},
  journal = {Archive of Formal Proofs},
  month   = apr,
  year    = 2022,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: BenOr_Kozen_Reif, Berlekamp_Zassenhaus, Design_Theory, Groebner_Bases, List-Index, Polynomial_Factorization