>>13269424>But then they also write A?1x for x?D(A?1) That's not too nice since the right expression is a proposition and the left one, one would think, is a vector.
I don't know. I think if you look into the references you may find a more basic elaboration that defines the terms
Which text?
>>13269250>>13269351So looking at
,
I found it convenient to factor out the j=1 case and write it as
,
where the the left factor (the function ) is
https://en.wikipedia.org/wiki/Q-Pochhammer_symboland the right hand factor then equals
,
where I is a multiset with the following multiplicities
{0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 0, 6: 1, 7: 0, 8: 1, 9: 1, 10: 1, 11: 0, 12: 2, 13: 0, 14: 1, 15: 1, 16: 2, 17: 0, 18: 2, 19: 0, 20: 2, 21: 1, 22: 1, 23: 0, 24: 3, 25: 1, 26: 1, 27: 1, 28: 2, 29: 0, 30: 3, 31: 0, 32: 2, 33: 1, 34: 1, 35: 1, 36: 4, 37: 0, 38: 1, 39: 1, 40: 3, 41: 0, 42: 3, 43: 0, 44: 2, 45: 2, 46: 1, 47: 0, 48: 4, 49: 1, 50: 2, 51: 1, 52: 2, 53: 0, 54: 3, 55: 1, 56: 3, 57: 1, 58: 1, 59: 0, 60: 5, 61: 0, 62: 1, 63: 2, 64: 3, 65: 1, 66: 3, 67: 0, 68: 2, 69: 1, 70: 3, 71: 0, 72: 5, ...}
or
0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1, 2, 0, 3, 0, 2, 1, 1, 1, 4, 0, 1, 1, 3, 0, 3, 0, 2, 2, 1, 0, 4, 1, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 5, 0, 1, 2, 3, 1, 3, 0, 2, 1, 3, 0, 5, 0, 1, 2, 2, 1, 3, 0, 4, 2, 1, 0, 5, 1, 1, 1, 3, 0, 5, 1, 2, 1, 1, 1, 5, 0, 2, 2, 4, 0, 3, 0, 3, 3, 1, ...
I checked
oeis.org for those values and for some mysterious reason, this is almost but not quite
>Number of ways to write n as n = x*y*z + x + y + z where 1 <= x <= y <= z <= n.(you can google it)
Pic related for the routine and a tool to evaluate it at any X, correctness not guarantted
