We prove that the number of cyclically symmetric, self-complementary plane partitions contained in a cube of side 2n equals the square of the number of totally symmetric, self-complementary plane partitions contained in the same cube, without explicitly evaluating either of these numbers. This appears to be the first direct proof of this fact. The problem of finding such a proof was suggested b...

this study aimed to evaluate the attitude of pediatricians toward the use of complementary and traditional medicine (tm) on children in muscat, oman. a cross-sectional survey was performed using a self-completed questionnaire during the year 2012. a total of 67 pediatricians, comprising of 30 males (44.8%) and 37 females (55.2%) participated in the study. the majority of the studied group (83.5...

We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by −1 as proposed by Kuperberg in [7, pp.25/26]. We use nonintersecting lattice path families to accomplish this for transpose–complementary, cyclically symmetric transpose–complement...

HEWLETT PACKARD finite fields; self-complementary basis; normal basis Explicit formulas are given for sets of relements forming a self-complementary norma basis of GF(q") over GF(q), where p is the characteristic of GF(q). Using these formulas, a straightforward construction of self-complementary bases for GF(qP"") over GF(q) is also presented.