Alternate solution to a discrete car parking problem

摘要

A few years ago, P. J. Flory lsqb;J. Am. Chem. Soc.61, 1518 (1939)rsqb; solved a statistical problem analogous to determining therandomhyphen;irreversiblesaturation formation of a 1times;2 overlayer on a linearnlattice, by deriving an expression for the fraction of empty lattice points. Methods are presented here for both the enumeration and construction of saturation configurations. This alternate approach is derived from the theory of partitions and incorporates shift and sumhyphen;rule operators for the calculation ofconfigurationalprobabilities. The fraction of filled lattice points is evaluated, and the configurational probabilities provide distribution functions for saturation configurations having different saturation levels (for fixedn). These distribution functions can be used to calculate sequence selective properties in addition to average saturation levels. Applications are illustrated in the analysis of the randomness of dehydrochlorination of polyvinylchloride and the distribution of UVhyphen;induced cyclobutylhyphen;thymine dimers inTetrahymenapyriformisDNA.