The Pascal Rhombus and the Stealth Configuration

TL;DR

This paper investigates the Pascal rhombus, a four-term variant of Pascal's triangle, and uses the stealth shape to prove four conjectures about its properties modulo 2, providing a unified approach.

Contribution

It introduces the stealth shape as a tool to prove conjectures about the Pascal rhombus modulo 2, offering a new unified proof method.

Findings

Proved four conjectures about the Pascal rhombus modulo 2

Demonstrated the utility of the stealth shape in combinatorial proofs

Unified the understanding of Pascal rhombus properties

Abstract

The Pascal rhombus is a variant of Pascal's triangle in which each term is a sum of four earlier terms. Klostermeyer et al. made four conjectures about the Pascal rhombus modulo 2. In this paper we show how exploration of the stealth shape leads to unified proofs of all of these conjectures.