Central Delannoy numbers and balanced Cohen-Macaulay complexes
The main goal of the present paper is to introduce a new join operation on colored simplicial complexes. By using this there are constructed balanced simplicial complexes as the balanced join of a balanced complex and a simplex such that the \(h\)-vector of the join is the \(f\)-vector of the original colored complex. The main result of the paper is Theorem 5.3, which states that the balanced join of two balanced Cohen-Macaulay simplicial complexes is Cohen-Macaulay. On the other hand, there is given an interesting example of the above operation. This establishes a connection between the well-known central Delannoy numbers and Legendre polynomials in a wider context.
scientific article; zbMATH DE number 5156890