The Minimal Sum of Squares Over Partitions with a Nonnegative Rank

Sela Fried

doi:10.1007/s00026-022-00625-z

The Minimal Sum of Squares Over Partitions with a Nonnegative Rank

Sela Fried

Research output: Contribution to journal › Article › peer-review

Abstract

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 m_n= Θ (n^{4 / 3}). Consequently, we improve by a factor of 2 the lower bound provided by Defant and Propp for iterates of order two.

Original language	English
Pages (from-to)	781-797
Number of pages	17
Journal	Annals of Combinatorics
Volume	27
Issue number	4
DOIs	https://doi.org/10.1007/s00026-022-00625-z
State	Published - 1 Dec 2023

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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abstract = "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.",

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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.

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The Minimal Sum of Squares Over Partitions with a Nonnegative Rank

Abstract

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