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 -