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k-regular Partitions

asked 2023-12-25 23:08:59 +0100

Tobi gravatar image

I'm looking for a code, to calculate the number of k-regular Partitions, of a positiv integer n. A k-regular Partition is a Partition, in which no summand is a multiple of k.

Hopefully someone has an idea! I am using the online Version of SageMath.

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answered 2023-12-26 00:09:14 +0100

Max Alekseyev gravatar image

You can use the standard Paritions() functionality by specifying allowed parts as not multiples of k below n:

def k_regular_partitions(n,k):
    return Partitions(n,parts_in=[i for i in range(1,n+1) if i%k]).cardinality()
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Asked: 2023-12-25 23:08:59 +0100

Seen: 129 times

Last updated: Dec 26 '23