Pascal Pyramids, Pascal Hyper-Pyramids and a Bilateral Multinomial Theorem

2003/11/04 by Martin Erik Horn, Horn, Martin Erik
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.math/0311035

6 pages, 3 figures

arxiv created 2003/11/04 · openalex publication_date 2003/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Part I: The two-dimensional Pascal Triangle will be generalized into a three-dimensional Pascal Pyramid and four-, five- or whatsoever-dimensional hyper-pyramids. Part II: The Bilateral Binomial Theorem will be generalised into a Bilateral Trinomial Theorem resp. a Bilateral Multinomial Theorem.

Related

• The Hockey Stick Theorems in Pascal and Trinomial Triangles
• Khayyam-Pascal Determinantal Arrays, Star of David Rule and Log-Concavity
• Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers
• A Triangular Array of the Counts of Natural Numbers with the Same Number of Prime Factors (Dimensions) Within 2n Space
• Bilateral binomial duplication formula