The Number H Sub n of Idempotent Elements in the Symmetric Semigroup on n Elements and the Asymptotic Expansion of H Sub n

摘要

The paper counts the number of idempotent elements H sub n in the symmetric semigroup. The exponential generating function of H sub n is obtained and a number of combinatorial identities and congruences are also given. The asymptotic expansion of H sub n is obtained. (Author)