Parts of measures and integer-valued transforms

Binomial transforms and integer partitions into parts of k different magnitudes

Arelationship between the general linear group of degree n over a finite field and the integer partitions of n into parts of k different magnitudes was investigated recently by the author. In this paper, we use a variation of the classical binomial transform to derive a new connection between partitions into parts of k different magnitudes and another finite classical group, namely the symplect...

Integer Valued AR(1) with Geometric Innovations

The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structu...

Transform coding with integer-to-integer transforms

A new interpretation of transform coding is developed that downplays quantization and emphasizes entropy coding, allowing a comparison of entropy coding methods with different memory requirements. With conventional transform coding, based on computing Karhunen–Loève transform coefficients and then quantizing them, vector entropy coding can be replaced by scalar entropy coding without an increas...

Limit computable integer parts

Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every r ∈ R, there exists an i ∈ I so that i ≤ r < i+ 1. Mourgues and Ressayre [11] showed that every real closed field has an integer part. In [6], it is shown that for a countable real closed field R, the integer part obtained by the procedure of Mourgues and Ressayre is ∆ωω (R). We would like ...

Reversible Integer-to-Integer Transforms and Symmetric Extension . . .