In mathematics, the **bicyclic semigroup** is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is usually referred to as simply a semigroup. The first published description of this object was given by Evgenii Lyapin in 1953. Alfred H. Clifford and Gordon Preston claim that one of them, working with David Rees, discovered it independently (without publication) at some point before 1943.

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**Bicyclic Semigroup**- Relation To Combinatorics

... The bicyclic monoid occurs in combinatorics, as the syntactic monoid of the Dyck language ... The Dyck language is the set of all strings of balanced pairs of parentheses, and thus finds common applications in defining binary trees and associative algebras ...