Determinants, choices and combinatorics
Copyright policy )Determinants, choices and combinatorics
We prove a formula which generalizes both Onn's colorful determinantal formula, related to Rota's basis conjecture, and Svrtan's $n!$ formula, related to the Atiyah-Sutcliffe problem. In some cases, our formula allows us to prove some results similar in spirit to the statement of Rota's basis conjecture. We prove such a result using Svrtan's $n!$ formula, generalizing one of Svrtan's arguments to a combinatorial setting.
- Notre Dame University – Louaize Lebanon
68Rxx, 15Axx, 05A05, 05Bxx, determinants, choices, Svrtan's \(n!\) formula, Combinatorial aspects of matroids and geometric lattices, linear independence, FOS: Mathematics, Mathematics - Combinatorics, Rota's basis conjecture, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Onn's colorful determinantal formula
68Rxx, 15Axx, 05A05, 05Bxx, determinants, choices, Svrtan's \(n!\) formula, Combinatorial aspects of matroids and geometric lattices, linear independence, FOS: Mathematics, Mathematics - Combinatorics, Rota's basis conjecture, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Onn's colorful determinantal formula
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