This article was prompted by Darryl Francis's article "Transposing the State Capital" in the November 2001 Word Ways. My apologies to Darryl for treading on his tail, but he lit upon a real challenge. I simply report what I found, but where Darryl has found other permutations (transpositions), I note those so that readers have one combined source. (He used sources other than those quoted below.) In addition, I include a number of plurals unearthed by Susan Thorpe.
"Permutations of United States Capitals,"
Word Ways: Vol. 35
, Article 9.
Available at: https://digitalcommons.butler.edu/wordways/vol35/iss1/9