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**Les preordres totaux compatibles avec un ordre partiel.**
*(French)*
Zbl 0343.06003

Math. et Sci. humaines 53, 5-30 (1976).

### MSC:

06A06 | Partial orders, general |

### 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.