TY - JOUR
T1 - Partitions with fixed differences between largest and smallest parts
AU - Andrews, George E.
AU - Beck, Matthias
AU - Robbins, Neville
N1 - Publisher Copyright:
© 2015 American Mathematical Society.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - We study the number p(n, t) of partitions of n with difference t between largest and smallest parts. Our main result is an explicit formula for the generating function Pt(q) := ∑n≥1 p(n, t) qn. Somewhat surprisingly, Pt(q) is a rational function for t > 1; equivalently, p(n, t) is a quasipolynomial in n for fixed t > 1. Our result generalizes to partitions with an arbitrary number of specified distances.
AB - We study the number p(n, t) of partitions of n with difference t between largest and smallest parts. Our main result is an explicit formula for the generating function Pt(q) := ∑n≥1 p(n, t) qn. Somewhat surprisingly, Pt(q) is a rational function for t > 1; equivalently, p(n, t) is a quasipolynomial in n for fixed t > 1. Our result generalizes to partitions with an arbitrary number of specified distances.
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U2 - 10.1090/S0002-9939-2015-12591-9
DO - 10.1090/S0002-9939-2015-12591-9
M3 - Article
AN - SCOPUS:84938263648
SN - 0002-9939
VL - 143
SP - 4283
EP - 4289
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 10
ER -