Log-concavity of subsequence counts of words

Abstract

Given a word over a finite alphabet, consider the sequence that counts, for each length, the number of distinct subsequences of that length. In 1976, Chase proved that this sequence is log-concave. His proof uses a triangular array indexed by the prefixes of the word together with a meticulous analysis of ratios of several sums. We instead decompose according to the first letter, which reduces the proof to a weighted average.