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The classic Dyck triangle, the Catalan triangle, and the Catalan convolutionmatrix are plane projections of the multidimensional Dyck triangle. In the Dyckpath, each node is uniquely determined by two of four interrelated parameters:(i) the position of the current parenthesis, (ii) the current unbalance of theparentheses, (iii) the number of viewed left parentheses, and (iv) the same forright parentheses. The last two parameters can be redefined, respectively, asthe index of the current Catalan number and the index of the summand in thedecomposition of the Catalan number into the sum of squares (Dyck squares). Forthe 4D Dyck triangle, we consider six 2D projections (some of them are not yetin demand) and four 3D projections.

4D Dyck triangle and its projections