An Empirical Formula Of S-2 Type Nested Order Statistics

Order statistics is a kind of important statistics in probability and statistics,the enumeration of SYT is an important topic in combinatorial mathematics.This paper,equivalent the Truncated shifted staircase which delete a space from the lower left corner as the S-2 type nested order statistics,mainly discusses an empirical formula of S-2 type nested order statistics relates to the enumeration of the shifted staircase and distribution of nested order statistic.The paper considers the following nested multiple integral:hereThe results of G_n(n ? 6)are obtained and then get the following formulaFinally,this empirical formula is verified by the known results.