Simple unpublished combinatorial proofs (discovered independently) of Bousfield, Curtis, and Singer are given of various lambda algebra results.

When Clenshaw Curtis rules are used to form a sparse grid, the orders of the underlying 1D factor rules form an exponential series. Even for a relatively low level, the 1D order growth is unnecessary, and is reflected in a noticeable cost in the order of the resulting sparse grid. We consider the effect of using the Clenshaw Curtis rules in a way that maintains the nestedness but delays their e...