Sur les partitions non croisées d’un cycle. (The non-crossed partitions of a cycle). (French) Zbl 0231.05014
Online Encyclopedia of Integer Sequences:
Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).
Number of crossing set partitions of {1,2,...,n}.
Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n whose ascent lengths form the k-th partition of the integer n; the partitions of n are ordered in the ”Mathematica” ordering.
Coefficients T(j, k) of a partition transform for Lagrange compositional inversion of a function or generating series in terms of the coefficients of the power series for its reciprocal. Enumeration of noncrossing partitions and primitive parking functions. T(n,k) for n >= 1 and 1 <= k <= A000041(n-1), an irregular triangle read by rows.
Regular triangle read by rows where T(n,k) is the number of non-crossing set partitions of {1, ..., n} in which all blocks have size k.
Number of non-crossing set partitions whose block sizes are the prime indices of n.
The number of maximal antichains in the Kreweras lattice of non-crossing set partitions of an n-element set.
The number of antichains in the Kreweras lattice of non-crossing set partitions of an n-element set.
References:
[1] | Cayley, A., On the partitions of a polygon, Phil. Mag., 4, 22, 237-262 (1890-1891) · JFM 23.0541.01 |
[2] | Kreweras, G., Une famille d’identités mettant en jeu toutes les partitions d’un ensemble fini de variables en un nombre Jonné de classes, C.R. Acad. Sci. Paris, 270, 1140-1143 (1970) · Zbl 0196.02602 |
[3] | Kreweras, G., Sur les éventails de segments, Cahiers B.U.R.O., 15, 16-22 (1970) |
[4] | Poupard, Y., Codage et dènombrement de diverses structures apparentées à celle d’arbre, Cahiers B.U.R.O., 16, 71-80 (1970) |
[5] | Raney, G. N., Functional composition patterns and power series reversion, Trans. Am. Math. Soc., 94, 441-451 (1960) · Zbl 0131.01402 |
[6] | Riordan, J., Combinatorial identities, ((1968), Wiley: Wiley New York), 148 · Zbl 0194.00502 |
[7] | Rota, G. C., On the foundations of combinatorial theory, I: Theory of Mobius functions, Z. Wahrscheinlichkeitstheorie u. Verw. Gebiete, 2, 340-368 (1964) · Zbl 0121.02406 |
[8] | Schroder, E., Vier kombinatorische Probleme, Z. Math. Phys., 15, 361-376 (1870) · JFM 02.0108.04 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.