Cosi Fan Tutte

Managing Identities Using Blockchains and CoSi

Magnetic properties of single-crystalline CoSi nanowires.

We have observed unusual ferromagnetic properties in single-crystalline CoSi nanowire ensemble, in marked contrast to the diamagnetic CoSi in bulk. High-density freestanding CoSi nanowires with B20 crystal structure are synthesized by a vapor-transport-based method. The reaction of cobalt chloride precursor with a Si substrate produces high-aspect-ratio CoSi nanowires. The high-resolution trans...

Tutte Polynomials

Let ∆ be a finite sequence of n vectors from a vector space over any field. We consider the subspace of Sym(V) spanned by Q v∈S v, where S is a subsequence of ∆. A result of Orlik and Terao provides a doubly indexed direct sum of this space. The main theorem is that the resulting Hilbert series is the Tutte polynomial evaluation T (∆; 1 + x, y). Results of Ardila and Postnikov, Orlik and Terao,...

Computing Tutte Paths

Tutte paths are one of the most successful tools for attacking Hamiltonicity problems in planar graphs. Unfortunately, results based on them are non-constructive, as their proofs inherently use an induction on overlapping subgraphs and these overlaps hinder to bound the running time to a polynomial. For special cases however, computational results of Tutte paths are known: For 4-connected plana...

Tutte polynomials for trees

We define two two-variable polynomials for rooted trees and one twovariable polynomial for unrooted trees, all of which are based on the coranknullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees TI and T, are isomorphic if and only if f(T,) = f(T2). The corresponding ...