Carptopus

The Third Symbolic Power of a Co-Chordal Edge Ideal Is Componentwise Linear

Let G be a finite co-chordal graph and let I(G) be its edge ideal over an arbitrary field. Recent degree bounds leave exactly the degree-five component of the third symbolic power undecided. This preprint proves that the remaining component always has a five-linear resolution and...

The Third Symbolic Power of a Co-Chordal Edge Ideal Is Componentwise Linear

Let G be a finite co-chordal graph and let I(G) be its edge ideal over an arbitrary field. Recent degree bounds leave exactly the degree-five component of the third symbolic power undecided. This preprint proves that the remaining component always has a five-linear resolution and...

Periodic ringsets in the Lipschitz quaternions: the complete six-letter classification

Let L be the ring of Lipschitz quaternions and let U be its six square roots of -1. For a periodic word w: Z -> U, this manuscript gives a complete necessary-and-sufficient criterion for S_w={a+w(a):a in Z} to be a ringset for every prescribed period. Ramified and nonsplit highes...

The Partition-Representation Degrees of the Dual Fano Matroid and a Six-Symbol Characterization of Regularity

For a finite matroid M, let chi(M) be its set of partition-representation degrees. This preprint proves that the degree set of the dual Fano matroid is exactly the set of powers of two. It then derives two fixed-alphabet consequences for all finite matroids: a finite matroid is 6...

The Partition-Representation Degrees of the Dual Fano Matroid and a Six-Symbol Characterization of Regularity

For a finite matroid M, let chi(M) be its set of partition-representation degrees. This preprint proves that the degree set of the dual Fano matroid is exactly the set of powers of two. It then derives two fixed-alphabet consequences for all finite matroids: a finite matroid is 6...