Search results
Results from the WOW.Com Content Network
The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after Eugène Catalan, though they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by
Talk: Super Catalan number. Add languages. ... Print/export Download as PDF; Printable version; In other projects ...
Print/export Download as PDF; Printable version; In other projects ... Catalan number; Fuss–Catalan number; Central binomial coefficient;
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.
To change this template's initial visibility, the |state= parameter may be used: {{Classes of natural numbers | state = collapsed}} will show the template collapsed, i.e. hidden apart from its title bar. {{Classes of natural numbers | state = expanded}} will show the template expanded, i.e. fully visible.
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 only known Catalan pseudoprimes are: 5907, 1194649, and 12327121 (sequence A163209 in the OEIS) with the latter two being squares of Wieferich primes. In general, if p is a Wieferich prime, then p 2 is a Catalan pseudoprime.
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.