Title: Symbol Invariant of Partition and the Construction,
Abstract: The symbol is used to describe the Springer correspondence for the classical
groups. We propose equivalent definitions of symbols for rigid partitions in
the $B_n$, $C_n$, and $D_n$ theories uniformly. Analysing the new definition of
symbol in detail, we give rules to construct symbol of a partition, which are
easy to remember and to operate on. We introduce formal operations of a
partition, which reduce the difficulties in the proof of the construction
rules. According these rules, we give a closed formula of symbols for different
theories uniformly. As applications, previous results can be illustrated more
clearly by the construction rules of symbol.