Enumeration formulas for standard Young tableaux of nearly hollow rectangular shapes

This paper considers the enumeration problem of a generalization of standard Young tableau (SYT) of truncated shape. Let λ∖μ|{(i0,j0)} be the SYT of shape λ truncated by μ whose upper left cell is (i0,j0), where λ and μ are partitions of integers. The summation representation of the number of SYT of the truncated shape (n+k+2,(n+2)m+1)∖(nm)|{(2,2)} is derived. Consequently, three closed formulas for SYT of hollow shapes are obtained, including the cases of (i). m=n=1, (ii). k=0, and (iii). k=1,m=n. Finally, an open problem is posed.