It is proved that for a certain class of integer polytopes P the polynomial h(t ) which appears as the numerator in the Ehrhart series of P, when written as a rational function of t, is equal to the h-polynomial of a simplicial polytope and hence that its co-efficients satisfy the conditions of the g-theorem. This class includes the order polytopes of graded posets, previously studied by Reiner and Welker, and the Birkhoff polytope of doubly stochastic n × n matrices. In the latter case the unimodality of the coefficients of h (t ), which follows, was conjectured by Stanley in 1983.
Field experiments were conducted in 1973-1975 at Katerini, Greece, to determine the effects of nitrogen and potassium fertilization rates on the yield, value and chemical composition of Samsun tobacco (Nicotiana tabacum L. (cv. Samsun 53)) leaves. Nitrogen was applied at rates of 20, 40, 60 and 80 kg/ha and potassium at rates of 30, 60, 90 and 120 kg/ha. Leaf yield increased significantly as applied nitrogen increased from 20 to 40 kg/ha, whereas further increase of nitrogen to 60 or to 80 kg/ha resulted in an insignificant increase in leaf yield. There was a tendency for value/ha of tobacco to increase as nitrogen rate increased from 20 to 40 kg/ha. A further increase of nitrogen to 60 and 80 kg/ha tended to decrease the value of tobacco. Generally, burning capacity and percentage of total alkaloids, total nitrogen, calcium and magnesium increased significantly as applied nitrogen increased. Percentage leaf potassium tended to increase as rate of nitrogen increased. Leaf yield and value/ha tended to increase as applied potassium increased from 30 to 60 kg/ha, beyond which no further increase occurred. Burning capacity and concentration of leaf potassium tended to increase, whereas the percentage of total alkaloids and magnesium tended to decrease as the rate of potassium increased. Concentrations of nitrogen and calcium were not affected by potassium rates. Generally, for production of a good yield and quality of Samsun tobacco in soils similar to that of Katerini, Greece, the rate of applied nitrogen should be higher than 20 kg/ha but lower than 60 kg/ha, while the rate of applied potassium should be above 30 kg/ha and up to 90 kg/ha.