Kreweras, G. Les preordres totaux compatibles avec un ordre partiel. (French) Zbl 0343.06003 Math. et Sci. humaines 53, 5-30 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 Documents MSC: 06A06 Partial orders, general PDF BibTeX XML Full Text: Numdam EuDML Online Encyclopedia of Integer Sequences: Schroeder’s second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers. Antichains (or order ideals) in the poset 2*2*3*n or size of the distributive lattice J(2*2*3*n) Antichains (or order ideals) in the poset 2*2*4*n or size of the distributive lattice J(2*2*4*n) Antichains (or order ideals) in the poset 2*2*5*n or size of the distributive lattice J(2*2*5*n) Number of antichains (or order ideals) in the poset B_4 X [n]; or size of the distributive lattice J(B_4 X [n]). Triangle of Euler-Bernoulli or Entringer numbers read by rows: T(n,k) is the number of down-up permutations of n+1 starting with k+1. a(0)=0, a(n) = n*E(2n-1) for n >= 1, where E(n) = A000111(n) are the Euler (or up-down) numbers. Number of distributive lattices; also number of paths with n turns when light is reflected from 7 glass plates. Number of distributive lattices; also number of paths with n turns when light is reflected from 8 glass plates. Number of distributive lattices; also number of paths with n turns when light is reflected from 9 glass plates. Number of distributive lattices; also number of paths with n turns when light is reflected from 10 glass plates. Number of distributive lattices; also number of paths with n turns when light is reflected from 11 glass plates. Number of distributive lattices; also number of paths with n turns when light is reflected from 12 glass plates. Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, transposed and read by upward antidiagonals. Antichains (or order ideals) in the poset 2*2*2*n or size of the distributive lattice J(2*2*2*n). Triangle T(n,k) (n >= 2, k >= 1) of Raney numbers read by rows.