Derives exact four-variable height expansion for Dyck paths with area and water-capacity weights and proves the length radius of G(x,1,p,q) equals the minimum positive real denominator branch, plus a (1-s)^{2/3} accumulation law on the diagonal.
Deutsch, Dyck path enumeration,Discrete Mathematics204(1999), 167–202
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Area and water-capacity statistics for upper hulls of Dyck paths
Derives exact four-variable height expansion for Dyck paths with area and water-capacity weights and proves the length radius of G(x,1,p,q) equals the minimum positive real denominator branch, plus a (1-s)^{2/3} accumulation law on the diagonal.