i'm not a win10 user however "resource limits" can be set per application (and per user) on any modern OS. that means mathematica would not be able to hog (disk, cpu, maybe other) resources you need to keep your computer responsive.

as far as the mathematica notebook doing the calculation it would normal for it to appear not to respond

however, there are keys that "interrupt OR abort" the current calculation

the calculation may generate huge data quickly and be transferring the data to the front end (viewer window, which cannot take and view that much data quickly or at all). in the older mathematica (ie, version 4) the only remedy was to 'xkill' the front end and connect another (advanced usage) or quit and re-open mathematica

imho it should be easier than it was for mm 4.0

Thanks for sharing, could be a nice extension for the built-in PartitionsP...

The k parameter is quite easy to program, I think however that the s parameter is way way way more tricky. I think IntegerPartitions uses some recursive dynamic programming when s is given basically iterating in some fancy way... This will not be possible large k...

This problem might be very hard to calculate and requires some mathematical insight to calculate it, simply using IntegerPartitions won;t work for the coming decades as Ilian explained...

"IntegerPartitions[n, {k}] with n=900, k=100

That is an interesting example, because the number of such partitions is 4575606410347783724917707119. Since each of them will occupy a modest amount of memory (2496 bytes), you would need a computer with at least 1.14207 10^22 gigabytes of RAM.

Nice! But I think, a program should realize if it is running out of memory and terminate the calculus with an error message.