Equitable factorizations of Hamming shells

Equitable factorizations of Hamming shells

We construct a 1-factorization of the complement Σm of the linear Hamming code of length m = mr = 2 r − 1 in the m-cube Qm, for r ≥ 2, having the following equitable property: its component 1-factors intersect each Cayley parallel 1-factor of Qm at a constant number of edges, (namely 2r edges). In the way to that construction, we find an equitable mr−1-factorization of Σm formed by two factors ...

Equitable facto rtzations of Hamming shells *

We construct a l-factorizalion of the complement .E, of the linear Hamming code of length m:m,--2'-l in the z-cube Q^, for r ) 2,havitg the following equitable property: its component l-factors intersect each Cayley parallel l-factor of Q^ at a constant number of edges, (namely 2mr-r-t edges). In the way to that construction, we flnd an equitable m,-t-factorization of 2, formed by two factors Q...

k-equitable mean labeling

Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions

We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals infect those belonging to the same community with higher probability than individuals in other communities. In community models the nodal infection probabili...

Equitability Revisited: Why the ‘‘Equitable Threat Score’’ Is Not Equitable

In the forecasting of binary events, verification measures that are ‘‘equitable’’ were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weig...