The Redheffer Matrix of a Partially Ordered Set
Copyright policy )The Redheffer Matrix of a Partially Ordered Set
R. Redheffer described an $n\times n$ matrix of 0's and 1's the size of whose determinant is connected to the Riemann Hypothesis. We describe the permutations that contribute to its determinant and its permanent in terms of integer factorizations. We generalize the Redheffer matrix to finite posets that have a 0 element and find the analogous results in the more general situation.
- University of Pennsylvania United States
partially ordered set, Exact enumeration problems, generating functions, Matrix equations and identities, Determinants, permanents, traces, other special matrix functions, determinant, permanent, algebraic, identities, Group actions on posets, etc., combinatorics, Redneffer matrix, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A15, exact enumeration problems
partially ordered set, Exact enumeration problems, generating functions, Matrix equations and identities, Determinants, permanents, traces, other special matrix functions, determinant, permanent, algebraic, identities, Group actions on posets, etc., combinatorics, Redneffer matrix, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05A15, exact enumeration problems
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