We give a simple and natural proof of (an extension of) the identity P(k, l, n) = P2(k − 1, l − 1, n − 1). The number P(k, l, n) counts noncrossing partitions of {1, 2, . . ...
Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandom number generators do not exist. This famous result is...