The point of this note is to prove that the secrecy function attains its maximum at y = 1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Solé. Further, we will give a very simple method to verify or disprove the conjecture on any given unimodular lattice.

The conformal invariance of unimodular gravity survives quantum corrections, even in the presence of conformal matter. Unimodular gravity can actually be understood as a certain truncation of the full Einstein-Hilbert theory, where in the Einstein frame the metric tensor has unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is...

A tournament is unimodular if the determinant of its skew-adjacency matrix $1$. In this paper, we give some properties and constructions tournaments. $T$ with $S$ invertible $S^{-1}$ a tournament. spectral characterization tournaments given. Lastly, show that every $n$-tournament can be embedded in by adding at most $n - \lfloor\log_2(n)\rfloor$ vertices.