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For =, this is just two times the ordinary Catalan numbers, and for =, the numbers have an easy combinatorial description. However, other combinatorial descriptions are only known [ 17 ] for m = 2 , 3 {\displaystyle m=2,3} and 4 {\displaystyle 4} , [ 18 ] and it is an open problem to find a general combinatorial interpretation.
Download as PDF; Printable version ... The number of noncrossing partitions of a set of n elements is the nth Catalan number. ... number 4, pages 333–350, 1972 ...
There is a Catalan number of chord diagrams on a given ordered set in which no two chords cross each other. [2] The crossing pattern of chords in a chord diagram may be described by a circle graph , the intersection graph of the chords: it has a vertex for each chord and an edge for each two chords that cross.
Substituting k = 1 into this formula gives the Catalan numbers and substituting k = 2 into this formula gives the Schröder–Hipparchus numbers. [7] In connection with the property of Schröder–Hipparchus numbers of counting faces of an associahedron, the number of vertices of the associahedron is given by the Catalan numbers.
The following other wikis use this file: Usage on cs.wikipedia.org Catalanova čísla; Usage on de.wikipedia.org Catalan-Zahl; Diskussion:Catalan-Zahl
Whilst the above is a concrete example Catalan numbers, similar problems can be evaluated using Fuss-Catalan formula: Computer Stack : ways of arranging and completing a computer stack of instructions, each time step 1 instruction is processed and p new instructions arrive randomly.
The Catalan numbers are solutions to numerous counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the n th Catalan number is the number of full binary trees with n internal nodes, or n+1 leaves.
Talk: Super Catalan number. Add languages. ... Print/export Download as PDF; Printable version; In other projects ...