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1. Text link: Catalan number - Wikipedia Domain: en.wikipedia.org Link: https://en.wikipedia.org/wiki/Catalan_number Description: The classical Catalan number corresponds to the root system of type . The classical recurrence relation generalizes: the Catalan number of a Coxeter diagram is equal to the sum of the Catalan numbers of all its maximal proper sub-diagrams. See also |
2. Text link: Catalan Numbers | Brilliant Math & Science Wiki Domain: brilliant.org Link: https://brilliant.org/wiki/catalan-numbers/ Description: The Catalan numbers are a sequence of positive integers that appear in many counting problems in combinatorics. They count certain types of lattice paths, permutations, binary trees, and many other combinatorial objects. They satisfy a fundamental recurrence relation, and have a closed-form formula in terms of binomial coefficients. The first few Catalan numbers are ... |
3. Text link: Catalan Number -- from Wolfram MathWorld Domain: mathworld.wolfram.com Link: http://mathworld.wolfram.com/CatalanNumber.html Description: Catalan Number. The Catalan numbers on nonnegative integers are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular -gon be divided into triangles if different orientations are counted separately?" (Euler's polygon division problem). |
4. Text link: Numbers in Catalan - Omniglot Domain: omniglot.com Link: https://omniglot.com/language/numbers/catalan.htm Description: Numbers in Catalan. How to count in Catalan (català), a Romance language spoken mainly in Spain, Andorra and France. Key to abbreviations: m = masculine, f = feminine, sg = singular, pl = plural If any of the numbers are links, you can hear a recording by clicking on them. If you can provide recordings, please contact me. |
5. Text link: catalan - geometer.org Domain: www.geometer.org Link: http://www.geometer.org/mathcircles/catalan.pdf Description: The Catalan numbers also count the number of rooted binary trees with ninternal nodes. Illustrated in Figure 4 are the trees corresponding to 0≤ n≤ 3. There are 1,1,2, and 5of them. Try to draw the 14trees with n=4internal nodes. A rooted binary tree is an arrangement of points (nodes) and lines connecting them where there |
6. Text link: Catalan Numbers - George Mason University Domain: masc.cs.gmu.edu Link: http://masc.cs.gmu.edu/wiki/CatalanNumbers Description: Catalan Numbers Catalan Numbers are a sequence of natural numbers that occur in many combinatorial problems involving branching and recursion. Here's a list of only some of the many problems in combinatorics reduce to finding Catalan numbers: Catalan's problem - computing the number of binary bracketings of n tokens.; Counting boolean associations - Count the number of ways n factors can be ... |
7. Text link: Catalan Numbers - mathshistory.st-andrews.ac.uk Domain: mathshistory.st-andrews.ac.uk Link: http://mathshistory.st-andrews.ac.uk/Miscellaneous/CatalanNumbers/catalan.html Description: Among other things, the Catalan numbers describe the number of ways a polygon with n+2 sides can be cut into n triangles, the number of ways in which parentheses can be placed in a sequence of numbers to be multiplied, two at a time; the number of rooted, trivalent trees with n+1 nodes; and the number of paths of length 2n through an n-by-n ... |
8. Text link: How to Compute the Catalan Number? | Technology of Computing Domain: helloacm.com Link: https://helloacm.com/how-to-compute-the-catalan-number/ Description: The Catalan number as described here is one of the well-known combinatorial number that has quite a few applications. For example, C(n) can be used to count the number of unique binary search trees of N nodes. The Catalan numbers can be computed using the following equation: |