Permutation Classes of Polynomial Growth

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue of all such sets of forbidden permutations having three or fewer elements is provided together with bounds on the degrees of the associated enumerating polynomials.Comment: 17 pages, 4 figure

Pattern classes and priority queues

When a set of permutations comprising a pattern class C is submitted as input to a priority queue the resulting output is again a pattern class C'. The basis of C' is determined for pattern classes C whose basis elements have length 3, and is finite in these cases. An example is given of a class C with basis 2431 for which C is not finitely based

The Central Role of Credit Crunches in Recent Financial History

macroeconomics, credit

Infrared Absorption Associated with Strong Hydrogen Bonds

Several investigators have proposed that there exists a more or less unique relation between the O-O distance in O-H-O hydrogen bonds and the shift of O-H vibrational frequency. [1-5] However, the meager intensities of some bands which have been ascribed to this vibration (notably in nickel dimethyl-glyoxime and potassium dihydrogen phosphate) have made us a little skeptical of the correlation inthe case of very short, and possibly symmetrical, hydrogen bonds