Some inequalities from switching theory

k -Dimensional arrays of multiway switches are used to derive inequalities. (Analytic proofs are also given.) As an example, suppose 0 p, q, r, …; p+q+r+ … =1; l, m, n, …>1, S=lmn … . Interpreting p, q, r , … as probabilities that an individual switch be set in a coordinate direction, we derive k −1 p S/l ) l +(1− q S/m ) m +(1− r S/n ) n + …