Log - Concavity and Related Properties of the Cycle Index
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Log-Concavity and Related Properties of the Cycle Index Polynomials
Let An denote the n-th cycle index polynomial, in the variables Xj , for the symmetric group on n letters. We show that if the variables Xj are assigned nonnegative real values which are logconcave, then the resulting quantities An satisfy the two inequalities An−1An+1 ≤ An ≤ ( n+1 n ) An−1An+1. This implies that the coefficients of the formal power series exp(g(u)) are log-concave whenever tho...
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Let An denote the n-th cycle index polynomial, in the variables Xj , for the symmetric group on n letters. We show that if the variables Xj are assigned nonnegative real values which are logconcave, then the resulting quantities An satisfy the two inequalities An 1An+1 A2n n+1 n An 1An+1: This implies that the coe cients of the formal power series exp(g(u)) are log-concave whenever those of g(u...
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تاریخ انتشار 2007