Counting r× s rectangles in (Catalan) words
Abstract
Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers r and s, this statistic counts the number of occurrences of a rectangle of size r× s in the bargraph representation of a word. We find the bivariate generating function for the distribution on words of the number of r× s rectangles and the generating function for their total number over all words. We also obtain the analog results for Catalan words.
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