G^N vs. Solving Combinatorics Utilizzo e statistiche

G^N is a special calculator not just a game: This math app animates iterations of one or compositions of two multi-valued maps for free groups of in principle arbitrary finite rank in the abelian and non-commutative cases respectively (in this version the rank is restricted to values in between 2 and 11). Well-known examples of such multi-valued maps are permutations, for example the flip (x_1,x_2)->(x_2,x_1), in G^N we just write (1,2)->(2,1) and instead of the inverse we convenient flip the number. A more involved type of such a multi-valued map is the n+1 cycle defined by (1,...,n)->(-2-3-...-n-1,3,4,...,n,1), a non-trivial theorem. For example if n=2 this map is the hexagon (1,2)->(-2-1,1), this map applied twice reads (1,2)->(2,-2-1) and the third iteration is the identity map (1,2)->(1,2).
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Finally there is the app that provides all 6 variations of combinatorics with step by step solutions: - permutation without repetition: Arranging elements without repetition. - permutation with repetition: Arranging elements with repetition. - combination without repetition: Selecting elements without considering the order. - combination with repetition: Selecting elements with consideration of the order. - variation without repetition: Arranging elements with fixed length without repetition. - variation with repetition: Arranging elements with fixed length with repetition. You only have to enter your values k and n. The values must be entered as natural numbers. The only exception is the k value for permutation with repitition. This requires several k values, which must be entered separated by semicolons. All calculations are stored in the history. The final solution can be shared. [ Contents ] - all 6 variations of combinatorics - results are calculated and shown in detail - history to save the input - detailed solution - natural numbers are supported - option to remove advertisements [ Usage ] - there are fields for entering values using a special keyboard - multiple k values can be entered using the semicolon key - press the check mark button at the bottom right to start the calculation - if values are missing, the corresponding field is highlighted in yellow - if the values are incorrect, the affected field will be highlighted in red - a short message explains why a value is incorrect - the entries in the history can be deleted or sorted - if you select an entry in the history, it will be automatically loaded for the calculation - the whole history can be deleted by pressing a button - solutions can be shared
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G^N VS.
Solving Combinatorics

18icembre d, 2024