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On a Sierpiński Pascal Matrix Construction and Monic Irreducible Polynomials over Binary Finite Fields

Year: 2026

Type: preprint

Abstract: This research note presents a weighted matrix construction based on the parity pattern of Pascal's triangle modulo 2, represented by the Sierpiński Pascal matrix. By applying a binary carry characterization, the construction yields the sequence a(n) = (8n − 2n)/3, which coincides with the classical enumeration formula for monic irreducible cubic polynomials over GF(2n).

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23938829

Author: Hernández-Torres, Juan Camilo

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225242184

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