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Ultra logconcave sequences and negative dependence. (English) Zbl 0888.60013
A conjecture by Pemantle, that the convolution of ultra-logconcave sequences is ultra-logconcave, is proved. This is equivalent to the statement, that a suitable negative dependence property is preserved under the operation of sampling uniformly without replacement from two finite exchangeable Bernoulli sequences.

MSC:
60E05 Probability distributions: general theory
60C05 Combinatorial probability
60K99 Special processes
62H20 Measures of association (correlation, canonical correlation, etc.)
05A19 Combinatorial identities, bijective combinatorics
11B65 Binomial coefficients; factorials; \(q\)-identities
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