MathDB

9

Part of 2021 Girls in Math at Yale

Problems(1)

Girls in Math at Yale 2021 Problem 9: Ali Can't Pronounce Stuff

Source:

2/27/2021
Ali defines a pronunciation of any sequence of English letters to be a partition of those letters into substrings such that each substring contains at least one vowel. For example, A ∣ THEN ∣ A\text{A } \vert \text{ THEN } \vert \text{ A}, ATH ∣ E ∣ NA\text{ATH } \vert \text{ E } \vert \text{ NA}, ATHENA\text{ATHENA}, and AT ∣ HEN ∣ A\text{AT } \vert \text{ HEN } \vert \text{ A} are all pronunciations of the sequence ATHENA\text{ATHENA}. How many distinct pronunciations does YALEMATHCOMP\text{YALEMATHCOMP} have? (Y is not a vowel.)
Proposed by Andrew Wu, with significant inspiration from ali cy
Yalecollege