A Terrible Expansion of the Determinant

2015/09/11 by Erik Insko, Insko, Erik, Katie Johnson +3
Mathematics · Physics and Astronomy · #05A18 #05A40 #05E45 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO #msc:05A18 #msc:05A40 #msc:05E45

paper · pdf · doi:10.48550/arxiv.1509.03647

11 pages, 7 figures

arxiv created 2015/09/11 · openalex publication_date 2015/09/11 · arxiv updated 2015/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

From a transfer formula in multivariate finite operator calculus, comes an expansion for the determinant similar to Ryser's formula for the permanent. Although this one contains many more terms than the usual determinant formula. To prove it, we consider the poset of ordered partitions, properties of the permutahedron, and some good old fashioned combinatorial techniques.

Citations

• Convex Polytopes and Enumeration

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