The part-frequency matrices of a partition

A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We prove results that suggest surprising usefulness for such a simple tool, including the existence of a related statistic that realizes every possible Ramanujan-type congruence for the partition function. To further exhibit its research utility, we give an easy generalization of a theorem of Andrews, Dixit and Yee on the mock theta functions. Throughout, we state a number of observations and questions that can motivate an array of investigations.Comment: Presented at the Kliakhandler Conference 2015, Algebraic Combinatorics and Applications, at Michigan Technological University. To appear in the Proceeding

Partitions into a small number of part sizes

We study $\nu_k(n)$, the number of partitions of $n$ into $k$ part sizes, and find numerous arithmetic progressions where $\nu_2$ and $\nu_3$ take on values divisible by 2 and 4. Expanding earlier work, we show $\nu_2(An+B) \equiv 0 \pmod{4}$ for (A,B) = (36,30), (72,42), (252,114), (196,70), and likely many other progressions for which our method should easily generalize. Of some independent interest, we prove that the overpartition function $\bar{p}(n) \equiv 0 \pmod{16}$ in the first three progressions (the fourth is known), and thereby show that $\nu_3(An+B) \equiv 0 \pmod{2}$ in each of these progressions as well, and discuss the relationship between these congruences in more generality. We end with open questions in this area.Comment: 11 pages; v2, small correction to proof of Theorem 7; v3, clean up some explanations, acknowledge recent results from Xinhua Xiong on overpartitions mod 16; v4, final journal version to appear International Journal of Number Theory (Feb. 2017

Congruences for 9-regular partitions modulo 3

It is proved that the number of 9-regular partitions of n is divisible by 3 when n is congruent to 3 mod 4, and by 6 when n is congruent to 13 mod 16. An infinite family of congruences mod 3 holds in other progressions modulo powers of 4 and 5. A collection of conjectures includes two congruences modulo higher powers of 2 and a large family of "congruences with exceptions" for these and other regular partitions mod 3.Comment: 7 pages. v2: added citations and proof of one conjecture from a reader. Submitted versio

Seeding of Strange Matter with New Physics

At greater than nuclear densities, matter may convert into a mixture of nucleons, hyperons, dibaryons, and strangelets, thus facilitating the formation of strange matter even before the onset of the quark-matter phase transition. From a nonstrange dibaryon condensate, it may even be possible to leapfrog into strange matter with a certain new interaction, represented by an effective six-quark operator which is phenomenologically unconstrained.Comment: 7 pages, no figure (Talk given at SQM97

Rural Health Insurance and Competitive Markets: Not Always Compatible?

Health Insurance, Rural Health, Health Markets, Competition, Health Policy, Health Economics and Policy,

OUTLOOK FOR U.S. AGRICULTURE

Production Economics,

Monitoring Processes with Changing Variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control

OUTLOOK FOR AGRICULTURE

Agricultural and Food Policy,