TY - JOUR
T1 - BIASES in INTEGER PARTITIONS
AU - Kim, Byungchan
AU - Kim, Eunmi
N1 - Publisher Copyright:
© 2021 Australian Mathematical Publishing Association Inc.
PY - 2021/10
Y1 - 2021/10
N2 - We show that there are biases in the number of appearances of the parts in two residue classes in the set of ordinary partitions. More precisely, let pj,k,m(n) be the number of partitions of n such that there are more parts congruent to j modulo m than parts congruent to k modulo m for m ≥2. We prove that p1,0,m(n) is in general larger than p0,1,m(n). We also obtain asymptotic formulas for p1,0,m(n) and p0,1,m(n) for m ≥ 2.
AB - We show that there are biases in the number of appearances of the parts in two residue classes in the set of ordinary partitions. More precisely, let pj,k,m(n) be the number of partitions of n such that there are more parts congruent to j modulo m than parts congruent to k modulo m for m ≥2. We prove that p1,0,m(n) is in general larger than p0,1,m(n). We also obtain asymptotic formulas for p1,0,m(n) and p0,1,m(n) for m ≥ 2.
KW - asymptotic formula
KW - bias
KW - partition
UR - https://www.scopus.com/pages/publications/85099566407
U2 - 10.1017/S0004972720001495
DO - 10.1017/S0004972720001495
M3 - Article
AN - SCOPUS:85099566407
SN - 0004-9727
VL - 104
SP - 177
EP - 186
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 2
ER -