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I am trying to add multiple criterion to

IntegerPartitions[n] 

so that it sorts only partitions that fit the criterion. It creates a list of list of numbers in descending orders and I want to eliminate all the ones that don't fit

• Has no part smaller than s

• part s occurs at most k times

• If elements are Dist apart then they are at least Diff apart
  i.e list[[i]] - list[[i+Dist]] >= Diff

• If parts are a distance d from each other and they are within c of other
  i.e if list[[i]] - list[[i + d]] <= c
  then the sum of the parts between them (and the parts themselves) is 'm' mod 'M'

I can do some individual conditions like getting part s to occur no more than k times, but I have trouble getting it to check all these conditions. Any help would be appreciated.

I am trying to add multiple criterion to

IntegerPartitions[n] 

so that it sorts only partitions that fit the criterion. It creates a list of list of numbers in descending orders and I want to eliminate all the ones that don't fit

• Has no part smaller than s (Already Solved)

• part s occurs at most k times (Already Solved)

• If elements are Dist apart then they are at least Diff apart
  i.e list[[i]] - list[[i+Dist]] >= Diff (Already Solved)

• If parts are a distance d from each other and they are within c of other
  i.e if list[[i]] - list[[i + d]] <= c
  then the sum of the parts between them (and the parts themselves) is 'm' mod 'M'

I can do some individual conditions like getting part s to occur no more than k times, but I have trouble getting it to check all these conditions. Any help would be appreciated.

EDIT: Thanks to LLlAMnYP for helping me get as far as I have. Now i have a list of list of integers in descending order and would just like to to filter out all the ones that don't fit the following criterion

• If parts are a distance d from each other and they are within c of other
  i.e if list[[i]] - list[[i + d]] <= c
  then the sum of the parts between them (and the parts themselves) is 'm' mod 'M'

I am trying to add multiple criterion to

IntegerPartitions[n] 

so that it sorts only partitions that fit the criterion. It creates a list of list of numbers in descending orders and I want to eliminate all the ones that don't fit

• Has no part bigger than s

• part s occurs at most k times

• If elements are Dist apart then they are at least Diff apart
  i.e list[[i]] - list[[i+Dist]] >= Diff

• If parts are a distance d from each other and they are within c of other
  i.e if list[[i]] - list[[i + d]] <= c
  then the sum of the parts between them (and the parts themselves) is 'm' mod 'M'

I can do some individual conditions like getting part s to occur no more than k times, but I have trouble getting it to check all these conditions. Any help would be appreciated.

I am trying to add multiple criterion to

IntegerPartitions[n] 

so that it sorts only partitions that fit the criterion. It creates a list of list of numbers in descending orders and I want to eliminate all the ones that don't fit

• Has no part smaller than s

• part s occurs at most k times

• If elements are Dist apart then they are at least Diff apart
  i.e list[[i]] - list[[i+Dist]] >= Diff

• If parts are a distance d from each other and they are within c of other
  i.e if list[[i]] - list[[i + d]] <= c
  then the sum of the parts between them (and the parts themselves) is 'm' mod 'M'

I can do some individual conditions like getting part s to occur no more than k times, but I have trouble getting it to check all these conditions. Any help would be appreciated.