Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity

Cristina Ballantine; Amanda Welch

Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity

Cristina Ballantine, Amanda Welch

Research output: Working paper › Preprint

Abstract

We consider the number of various partitions of $n$ with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that for $n\geq 5$ we have $p_{od}^{eu}(n)

Original language	Undefined/Unknown
State	Published - May 31 2024

Keywords

math.CO
math.NT
05A17, 05A20, 11P81

Access to Document

2406.00139v1

Cite this

@techreport{e5540cdf34a94ab8bb305624c5ac75d0,

title = "Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity",

abstract = " We consider the number of various partitions of \$n\$ with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that for \$n\textbackslash{}geq 5\$ we have \$p\_\{od\}\textasciicircum{}\{eu\}(n)",

keywords = "math.CO, math.NT, 05A17, 05A20, 11P81",

author = "Cristina Ballantine and Amanda Welch",

year = "2024",

month = may,

day = "31",

language = "Undefined/Unknown",

type = "WorkingPaper",

}

TY - UNPB

T1 - Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity

AU - Ballantine, Cristina

AU - Welch, Amanda

PY - 2024/5/31

Y1 - 2024/5/31

N2 - We consider the number of various partitions of $n$ with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that for $n\geq 5$ we have $p_{od}^{eu}(n)

AB - We consider the number of various partitions of $n$ with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that for $n\geq 5$ we have $p_{od}^{eu}(n)

KW - math.CO

KW - math.NT

KW - 05A17, 05A20, 11P81

M3 - Preprint

BT - Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity

ER -