Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Generate the zero-free compositions of a positive integer
ResourceFunction["StrictIntegerCompositions"][n] gives a list of all possible ways to form a composition of the integer n into smaller integers. | |
ResourceFunction["StrictIntegerCompositions"][n,k] gives compositions using at most k integers. | |
ResourceFunction["StrictIntegerCompositions"][n,{k}] gives compositions into exactly k integers. | |
ResourceFunction["StrictIntegerCompositions"][n,{kmin,kmax}] gives compositions into between kmin and kmax integers. | |
ResourceFunction["StrictIntegerCompositions"][n,kspec,{s1,s2,…}] gives compositions involving only the numbers si. | |
ResourceFunction["StrictIntegerCompositions"][n,kspec,sspec,m] limits the result to using only first m partitions. |
All the strict compositions of an integer:
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All the strict compositions of 5:
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The compositions of 5 into at most three integers:
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Compositions that involve only 1, 2 and 4:
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Compositions of even length only:
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Ways to form 3 from any of five given rational numbers:
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Limit the number of results:
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There are 2n-1 strict compositions of n:
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Each composition adds up to the original number:
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StrictIntegerCompositions gives the permutations of compositions returned by IntegerPartitions:
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Results of StrictIntegerCompositions do not include zeros, whereas results of the resource function IntegerCompositions do:
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Unlike the resource function IntegerCompositions, StrictIntegerCompositions does not necessarily give compositions in canonical order:
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StrictIntegerCompositions cannot give an infinite list of compositions:
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Get a finite list instead:
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There are no strict compositions of 1/2:
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There are, however, compositions into rationals:
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If all items requested by the fourth argument are not present, as many as possible are returned:
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A compact way to show integer compositions:
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