Note of the enumeration formula of standard Young tableaux of truncated shape (nm)∖(2)(nm)∖(2)

In this paper integration method is used to derive the enumeration formulas of the standard Young tableau (SYT) of truncated shape. An integration representation of the number of SYT of truncated shape (nm)∖(2)(nm)∖(2) is given, which implies a positive proof of the conjecture of Adin et al. on the number of SYT of truncated shape (nn)∖(2)(nn)∖(2). Furthermore, the enumeration formulas of the numbers of SYTs of truncated shapes (nn−k)∖(2)(nn−k)∖(2) and (nn−k)∖(1,1)(nn−k)∖(1,1)(k=1,2)(k=1,2) have been obtained.