[seqfan] Re: Modular Partitions

William Keith william.keith at gmail.com
Wed Apr 30 23:03:23 CEST 2014


This seems to be a popular kind generalization of partitions.

I considered the number of partitions of n in which no subsum is 0 mod N.
This puts a limit on the number of possible parts (N - gcd(n,N)).  If N is
a prime, the number of such "modpartitions" of N of length N-k is the sum
of the partition numbers p(0) + p(1) + ... + p(k-1) for k<N/3.  Data
suggest that the count is exact up to k<N/2, but if I understand correctly
this is an open question in an area known as zero-sumfree sequences.

I shall consider your symmetry in n and k.

William Keith



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