On Primitive 3-smooth Partitions of n

Counting Partitions of a Fixed Genus

We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus is finite. We illustrate our method by finding the generating function for genus 2 ...

Partition theorems for factorisations of ascending parameter words

We prove, in primitive recursive arithmetic, an extension of a theorem established by Milliken and independently by Neget~il and R6dl on partitions of fixed rank partitions of a finite set. In this way we depict the preservation of structure under partitions of the outcomes of substitution systems, which can also undergo various stage transitions.

Enumeration of Partitions by Long Rises, Levels, and Descents

When the partitions of [n] = {1, 2, . . . , n} are identified with the restricted growth functions on [n], under a known bijection, certain enumeration problems for classical word statistics are formulated for set partitions. In this paper we undertake the enumeration of partitions of [n] with respect to the number of occurrences of rises, levels and descents, of arbitrary integral length not e...

Differential transformation method for solving fuzzy differential inclusions by fuzzy partitions

The relaxant effect of Nigella sativa on smooth muscles, its possible mechanisms and clinical applications

Nigella sativa (N. sativa) is a spice plant which has been traditionally used for culinary and medicinal purposes. Different therapeutic properties including the beneficial effects on asthma and dyspnea, digestive and gynecology disorders have been described for the seeds of N. sativa. There is evidence of the relaxant effects of this plant and some of its constituents on different types of smo...