No Conformal Anomaly in Unimodular Gravity

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 enjoys unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is consistent as well.Comment: 20 pages; misprints correcte

Marked chain-order polytopes

We introduce in this paper the marked chain-order polytopes associated to a marked poset, generalizing the marked chain polytopes and marked order polytopes by putting them as extremal cases in an Ehrhart equivalent family. Some combinatorial properties of these polytopes are studied. This work is motivated by the framework of PBW degenerations in representation theory of Lie algebras.Comment: 18 pages, title changed, the relation to string polytopes is remove

Doppler Tolerance, Complementary Code Sets and the Generalized Thue-Morse Sequence

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-Calderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.Comment: 12 page

Systems theoretic methods in decoding

In this paper we show how ideas based on system theoretic modeling of linear behaviors may be used for decoding of linear codes. In particular we show how Sudan's bivariate interpolation approach to list decoding of RS codes allows a system theoretic interpretation