On certain unimodal sequences and strict partitions

TL;DR

This paper explores the enumeration of specific unimodal sequences and strict partitions, refining their counts based on certain parameters by leveraging a bijection and sum properties.

Contribution

It introduces a refined enumeration method for strict partitions and unimodal sequences using a bijection and sum conditions, advancing combinatorial enumeration techniques.

Findings

Enumeration of unimodal sequences with zero alternating sum

Refined counts of strict partitions by parts and BG-rank

Utilization of Vandervelde's bijection for enumeration

Abstract

Building on a bijection of Vandervelde, we enumerate certain unimodal sequences whose alternating sum equals zero. This enables us to refine the enumeration of strict partitions with respect to the number of parts and the BG-rank.