Partitions with fixed differences between largest and smallest parts

We study the number $p(n,t)$ of partitions of $n$ with difference $t$ between largest and smallest parts. Our main result is an explicit formula for the generating function $P_t(q) := \sum_{n \ge 1} p(n,t) \, q^n$. Somewhat surprisingly, $P_t(q)$ is a rational function for $t>1$; equivalently, $p(n,t)$ is a quasipolynomial in $n$ for fixed $t>1$. Our result generalizes to partitions with an arbitrary number of specified distances.Comment: 5 page

The Quest of the Sacred Ginkgo

"My attention was called to this amazing tree when as an amateur collector of fossil woods and leaves I came upon the fascinating account of Dr. Merriam concerning the discovery of a fossil ginkgo leaf still enclosed within its mold in the vicinity of Bonneville, Oregon.

LIFE HISTORY of the GINKO PETRIFIED FOREST or The Autobiography of an Ancient Oak Tree

An account of a fossilized log at Ginkgo Tree State Park written by the man who discovered the fossil trees and established there were Ginkgo trees in North America in the distant past. The booklet is written from the perspective of one of the fossilized trees, tracing the geologic forces that led to it becoming a fossil

Downy brome (Bromus tectorum) and Japanese brome (Bromus japonicus) biology, ecology, and management: literature review

Date inferred from file name.Includes bibliographical references

Downy brome (Bromus tectorum) and Japanese brome (Bromus japonicus) biology and management

Date inferred from file name

New tools and new tests in comparative political economy - the database of political institutions

This paper introduces a large new cross-country database on political institutions: the Database on Political Institutions (DPI). The authors summarize key variables (many of them new), compare this data set with others, and explore the range of issues for which the data should prove invaluable. Among the novel variables they introduce: 1) Several measures of tenure, stability, and checks and balances. 2) Identification of parties with the government coalition or the opposition. 3) Fragmentation of opposition and government parties in legislatures. The authors illustrate the application of DPI variables to several problems in political economy. Stepan and Skach, for example, find that democracy is more likely to survive under parliamentary governments than presidential systems. But this result is not robust to the use of different variables from the DPI, which raises puzzles for future research. Similarly, Roubini and Sachs, find that divided governments in the OECD run higher budget deficits after fiscal shocks. Replication of their work using DPI indicators of divided government indicates otherwise, again suggesting issues for future research. Among questions in political science and economics, that this database may illuminate: the determinants of democratic consolidation, the political conditions for economic reform, the political and institutional roots of corruption, and the elements of appropriate and institutionally sensitive design of economic policy.Decentralization,Parliamentary Government,National Governance,Information Technology,ICT Policy and Strategies,National Governance,Parliamentary Government,ICT Policy and Strategies,Information Technology,Governance Indicators