Distribution Of The Hollow Nested Order Statistics Of The Shape Of Approximately Rectangular Hexagon

Order statistics is an important research topic of probability statistics.Recent studies have shown that the probability distribution of nested order statistics has a corresponding internal relationship with the enumeration of standard Young tableaux.This paper investigates the hollow SYT chart of the approximately rectangular hexagon.First,a variable in the nested model is integrated,and then the nested simplex is transformed according to the situation.The enumeration formula of the SYT-type chart of shape((n+2)n+1,3)\(nm-1,1)|{(2,2)}(m,n≥2)is obtained by using multiple integrals and combinatorial identities.Further,the probability distribution of the hollow nested order statistics of the approximately rectangular hexagon is obtained,that is recorded as P(n+2)m+1,3)\(nm-1,1)|{(2,2)}(m,n≥2).Finally,by limiting the values m,n in the enumeration formula,we directly obtain the formula of the SYT-type chart of shape 3m+2\1m|{(2,2)},and some results are as follows.1.the probability distribution of nested order statistics of(4m+1,3)\(2m-0,1)|{(2,2)}(m≥2)is:2.the probability distribution of nested order statistics of((n+2)2,3)\(2,2)(n≥2)is(?)...