A poset structure on quasifibonacci partitions

TL;DR

This paper introduces a poset structure on partitions of integers into quasifibonacci numbers, explores their relations, and generalizes Robbins' result on quasifibonacci power series coefficients.

Contribution

It constructs a novel poset framework for quasifibonacci partitions and extends Robbins' theorem to a broader context.

Findings

Poset structure on quasifibonacci partitions

Symmetric and recursive relations between posets

Generalization of Robbins' result

Abstract

In this paper, we study partitions of positive integers into distinct quasifibonacci numbers. A digraph and poset structure is constructed on the set of such partitions. Furthermore, we discuss the symmetric and recursive relations between these posets. Finally, we prove a strong generalization of Robbins' result on the coefficients of a quasifibonacci power series.