OFFSET
3,2
COMMENTS
A truncated ST-pair O(q^n) consists of a subset S of {1, 2, ..., n-1} and a subset T of {1, 2, ..., n-2} such that (Product_{k in S} 1/(1-q^k)) - q (Product_{k in T} 1/(1-q^k)) = 1 + O(q^n). - Andrey Zabolotskiy, Feb 27 2024
REFERENCES
F. G. Garvan, Shifted and Shiftless Partition Identities, in Number Theory for the Millennium II (M. A. Bennett et al., eds.), AK Peters, Ltd. 2002, pp. 75-92.
LINKS
F. G. Garvan, Shifted and shiftless partition identities (2001).
MATHEMATICA
st[n_] := Select[Flatten[Table[{s, t}, {s, Subsets@Range[n - 1]}, {t, Subsets@Range[n - 2]}], 1], Normal[Product[1/(1-q^k) + O[q]^n, {k, First@#}] - q Product[1/(1-q^k) + O[q]^n, {k, Last@#}] - 1] == 0 &];
Table[Length@st[n], {n, 3, 9}] (* Andrey Zabolotskiy, Feb 27 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Barry Cipra, Jun 15 2004
STATUS
approved