Hypergeometric identities associated with statistics on words
نویسندگان
چکیده
The purpose of this note is to show how combinatorial arguments can produce nontrivial identities between hypergeometric q-series in two variables. This will be illustrated by using as examples 1. the major index of a binary word 2. the Durfee square size of an integer partition 3. the number of inversions in a binary word 4. the number of descents in a binary word 5. the sum of the positions of the 0’s in a bitstring 6. “lecture hall” statistics on words. Let w be a word of length n over the alphabet {0, 1} (a binary word). By the major index of w we mean the sum of those indices j, 1 ≤ j ≤ n − 1, for which wj > wj+1, i.e.,
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