The [23,14,5] Wagner code is unique

The Mermin-Wagner Theorem

LetA be a C∗ algebra such as the algebra of quasi-local observables of a quantum spin system on Z, and suppose {αt}t∈R is a strongly continuous one-parameter group of automorphisms of A, which we will refer to as the dynamics of the system. The examples we have in mind are the dynamics of a quantum spin system generated by a not-too-long-range interaction Φ, e.g., one that satsifies, for some λ...

Mass murder: the Wagner case.

The IRMA code for unique classification of medical images

Modern communication standards such as Digital Imaging and Communication in Medicine (DICOM) include nonimage data for a standardized description of study, patient, or technical parameters. However, these tags are rather roughly structured, ambiguous, and often optional. In this paper, we present a mono-hierarchical multi-axial classification code for medical images and emphasize its advantages...

On the Livingstone-Wagner Theorem

Let G be a permutation group on the set Ω and let S be a collection of subsets of Ω, all of size ≥ m for some integer m . For s ≤ m let ns(G, S) be the number of G-orbits on the subsets of Ω which have a representative y ⊆ x with |y| = s and y ⊆ x for some x ∈ S . We prove that if s < t with s + t ≤ m then ns(G, S) ≤ nt(G, S) . A special case of this theorem is the Livingstone-Wagner Theorem wh...

The Continuum is Countable: Infinity is Unique

Since the theory developed by Georg Cantor, mathematicians have taken a sharp interest in the sizes of infinite sets. We know that the set of integers is infinitely countable and that its cardinality is א0. Cantor proved in 1891 with the diagonal argument that the set of real numbers is uncountable and that there cannot be any bijection between integers and real numbers. Cantor states in partic...