Counting lattice paths in restricted planes (Q1971209)

The author proves a complicated formula for the number of lattice paths of fixed length on a square lattice, contained in the plane sector \(0\leq y\leq x\), as well as for paths of this kind that do not cross the line \(y=-x+ a\) \((a>0)\). In the proofs the techniques of enumeration of noncrossing paths [see \textit{I. M. Gessel} and \textit{X. Viennot}, Adv. Math. 58, 300-321 (1985; Zbl 0579.05004)] and of Young tableaux [compare \textit{D. Gouyou-Beauchamps}, Eur. J. Comb. 10, No. 1, 69-82 (1989; Zbl 0672.05012)] are used. Some expressions involve Catalan numbers.