C Sequential Optimization Numbers Group

TL;DR

This paper introduces C sequential optimization numbers, linking them to Stirling numbers of the first kind, and explores their properties, recurrence relations, and bounds, expanding the understanding of these combinatorial numbers.

Contribution

It defines C sequential optimization numbers and connects them to Stirling numbers of the first kind, providing new properties and bounds.

Findings

Unsigned Stirling numbers of first kind are (0,1) sequential optimization numbers.

Recurrence formulas for C sequential optimization numbers are established.

Upper bounds for C sequential optimization numbers are derived.

Abstract

We define C sequential optimization numbers, where C is a k+1-tuple vector. We prove that the unsigned Stirling numbers of first kind are (0,1) sequential optimization numbers. Many achievements of the Stirling numbers of first kind can be transformed into the properties of C sequential optimization numbers. We give some examples such as the recurrence formula and an instance of C sequential optimization numbers. We also extend some properties such as an upper bounder of them.