Place the director Billy Wilder at one end of the chain, and the composer Vernon Duke at the other.

What two other well-known Hollywood figures manage to constitute the links  between Wilder and Duke?

And what is it that connects the two,for the moment  unnamed men, in the middle?

Show your work.

__________________________

As a week has gone by, it's time for the answer.

Here it is:

Billy Wilder had a writing partner, I. A. L. Diamond, with whom he wrote the scripts for many of his movies, including "The Apartment" and "Some Like It Hot".

I. A. L. Diamond was born Iţec (Itzek) Domnici in Ungheni, Iaşi County, Bessarabia, Romania, present day Moldova, was referred to as "Iz" in Hollywood, and was known to quip that his initials stood for "Interscholastic Algebra League".

It wasn't just a quip, but the truth. He had attended Boys High in Brooklyn in the 1930s, at a time when Boys High was one of the best high schools in New York, and when its Math Team, and the school math paper, The Euclidean, were unrivalled. He took part in

Wikipedia contains this capsule biography:

He was born Iţec (Itzek) Domnici in Ungheni, Iaşi County, Bessarabia, Romania, present day Moldova, was referred to as "Iz" in Hollywood, and was known to quip that his initials stood for "Interscholastic Algebra League". [it wasn't just a "quip" but the truth; when he felt he needed to flesh out his name, he took those initials from the mathematics competition that had such an important part of his high school life].]

Diamond emigrated with his family to the Crown Heights area of Brooklyn in the United States at the age of 9. There he studied at the Boy's High School, showing ability in mathematics, competing in the state Mathematics Olympiads in 1936-37, winning several gold medals.

Diamond completed his undergraduate studies at Columbia in 1941. There he studied journalism, publishing in the Columbia Daily Spectator under the pseudonym "I.A.L. Diamond".

The next figure on this American Isnad-Chain is the song-writer Yip Harburg. Like I.A.L. Diamond, he had changed his name. Wiki: Harburg, the youngest of four surviving children (out of ten), was born Isidore Hochberg on the Lower East Side of New York City on April 8, 1896....Harburg's nickname "Yipsel" (often shortened to "Yip") came about as "Yipsel" is how people pronounced "YPSL" -- the acronym for the Young People's Socialist League of which he was a member.

That is what links I.A.L. Diamond to Yip Harburg -- the initials, respectively, of the Interscholastic Algebra League and the Young People's Socialist League, which became part of their show-business names.

What allows us to go Yip Harburg to Vernon Duke? Well, Vernon Duke also changed his name. He was born as Vladimir Dukelsky:

"Vladimir Aleksandrovich Dukelsky (Russian: Владимир Александрович Дукельский) was born in 1903 into a noble family of mixed Georgian-Austrian-Spanish-Russian descent, in Parafianovo, Belarus, then part of the Russian Empire. The 1954 Grove's Dictionary of Music and Musicians referred to "one of his grandparents" (Princess Tumanishvili) as having been "directly descended from the kings of Georgia". His birthplace, however, was a small railroad station in Minsk Governorate. At that time his mother "happened to be traveling by train".^[ The Dukelskys resided in Kiev, and Vladimir's only visit to Saint Petersburg and Moscow occurred in the summer of 1915. The impressions of that remarkable summer were later echoed in Dukelsky's most daring classical composition, the Russian oratorio The End of St. Petersburg (1931–1937).

At the age of 11, Dukelsky was admitted to the Kiev Conservatory where he studied composition with Reinhold Glière and musical theory with Boleslav Yavorsky. In 1919, his family escaped from the turmoil of civil war in Russia and spent a year and a half with other refugees in Constantinople. In 1921 they obtained American visas and sailed steerage class on the SS King Alexander to New York; immigrating at Ellis Island, where his name was recorded as Vladimir Doukelsky in the French fashion. It was in 1922 in New York that George Gershwin befriended the young immigrant; Gershwin (himself born Jacob Gershowitz) suggested Dukelsky truncate and americanize his name. Dukelsky's first songs published under his nom de plume were conceived that year, but he continued to write classical music and Russian poetry under his given name until 1955."

But the main thing is that Vernon Duke, and Yip Harburg, were collaborators on many songs, including those for "April in Paris" and "Ziegfeld Follies of 1934," just as Billy Wilder and I.A.L. Diamond were collaborators on many movies.

That's the answer.

I've shown my work.