Carptopus

Realizability and Minimum Dimension of Fano Half-Rank Profiles over F2

Let V be a finite-dimensional vector space over F2 and let a three-parameter linear family of alternating bilinear forms define seven half-ranks on the Fano plane. This manuscript classifies exactly which labelled nonnegative integer profiles are realizable in some ambient dimens...

Exact Regions and Low-Polar-Rank Recursion in the Third Support Spectrum of Binary Second-Order Reed--Muller Codes

This manuscript studies support sizes of three-dimensional subcodes of binary second-order Reed--Muller codes. It proves two sharp all-dimensional spectrum gaps, determines the exact spectra through nine variables, classifies the complete near-full interval, gives a finite sound-...

Exact Regions and Low-Polar-Rank Recursion in the Third Support Spectrum of Binary Second-Order Reed--Muller Codes

This manuscript studies support sizes of three-dimensional subcodes of binary second-order Reed--Muller codes. It proves two sharp all-dimensional spectrum gaps, determines the exact spectra through nine variables, classifies the complete near-full interval, gives a finite sound-...

Projective-plane triangulations yield orderable cographic matroids

We prove that the cographic matroid of the 1-skeleton of every finite simplicial triangulation of the real projective plane is orderable. Starting from the six-vertex triangulation with 1-skeleton K6 and repeatedly applying stellar subdivision gives infinitely many 3-connected, r...

Projective-plane triangulations yield orderable cographic matroids

We prove that the cographic matroid of the 1-skeleton of every finite simplicial triangulation of the real projective plane is orderable. Starting from the six-vertex triangulation with 1-skeleton K6 and repeatedly applying stellar subdivision gives infinitely many 3-connected, r...

Realizability and Minimum Dimension of Fano Half-Rank Profiles over F2

Let V be a finite-dimensional vector space over F2 and let a three-parameter linear family of alternating bilinear forms define seven half-ranks on the Fano plane. This manuscript classifies exactly which labelled nonnegative integer profiles are realizable in some ambient dimens...