Bóna, Miklós The permutation classes equinumerous to the smooth class. (English) Zbl 0899.05001 Electron. J. Comb. 5, Research paper R31, 12 p. (1998); printed version J. Comb. 5, 469-480 (1998). The author determines all permutation classes defined by pattern avoidance that have the same cardinality as the class of permutations having a smooth Schubert variety. A lattice path interpretation is given. Reviewer: R.Stanton (Winnipeg) Cited in 13 Documents MSC: 05A05 Permutations, words, matrices 05E10 Combinatorial aspects of representation theory 14M15 Grassmannians, Schubert varieties, flag manifolds Keywords:permutation classes; pattern avoidance; smooth Schubert variety; lattice path PDFBibTeX XMLCite \textit{M. Bóna}, Electron. J. Comb. 5, No. 1, Research paper 31, 12 p. (1998; Zbl 0899.05001) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when on the diagonal, (1,1). Number of permutations of length n which avoid the patterns 2143, 1324 (smooth permutations); or avoid the patterns 1342, 2431; etc.