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Sci."],"published-print":{"date-parts":[[2022,4]]},"abstract":"<jats:p> We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete Applied Mathematics, 2014). We extend to any number of distinct abelian borders a result of Rampersad et al. (Developments in Language Theory, 2013) on the exact number of binary words of a given length with no abelian borders. 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