TY - JOUR
T1 - The Minimal Sum of Squares Over Partitions with a Nonnegative Rank
AU - Fried, Sela
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2023/12/1
Y1 - 2023/12/1
N2 - Motivated by a question of Defant and Propp (Electron J Combin 27:Article P3.51, 2020) regarding the connection between the degrees of noninvertibility of functions and those of their iterates, we address the combinatorial optimization problem of minimizing the sum of squares over partitions of n with a nonnegative rank. Denoting the sequence of the minima by (mn)n∈N, we prove that mn= Θ (n4 / 3). Consequently, we improve by a factor of 2 the lower bound provided by Defant and Propp for iterates of order two.
AB - Motivated by a question of Defant and Propp (Electron J Combin 27:Article P3.51, 2020) regarding the connection between the degrees of noninvertibility of functions and those of their iterates, we address the combinatorial optimization problem of minimizing the sum of squares over partitions of n with a nonnegative rank. Denoting the sequence of the minima by (mn)n∈N, we prove that mn= Θ (n4 / 3). Consequently, we improve by a factor of 2 the lower bound provided by Defant and Propp for iterates of order two.
UR - https://www.scopus.com/pages/publications/85143241866
U2 - 10.1007/s00026-022-00625-z
DO - 10.1007/s00026-022-00625-z
M3 - Article
AN - SCOPUS:85143241866
SN - 0218-0006
VL - 27
SP - 781
EP - 797
JO - Annals of Combinatorics
JF - Annals of Combinatorics
IS - 4
ER -