An allusion is a casual reference to a well-known place,story, book, historical event or work of art. There are many literary and Biblical allusions in The Devil's Arithmetic.
When Hannah first meets Rachel and the girls at the wedding, she tells them stories and totally entertains them. The stories she tells them are current day movies, stories, and books.
"Stories seems to tumble out of Hannah's mouth, reruns of all the movies and books she could think of. She told the girls about Yentl and then about Conan the Barbarian with equal vigor; about Star Wars, which confused them; and Fiddler on the Roof, which did not. She told them the plot of Little Women in ten minutes, a miracle of compression, especially since her book report had been seven typed pages." (pg 50)
These are literary allusions since they are about movies and books. Jane Yolan is alluding to literary works that she feels the reader will know and make a connection. Another literary allusion is
"'So let me tell you about the Wizard of Oz' she said. She couldn't remember which was the movie and which was the book. Shrugging her shoulders. she began a strange mixture of the two, speeding along until the line 'Gosh, Toto, this sure doesn't look like Kansas." (pg 51)
This makes a literary allusion by not only giving the title of the book and movie but also by giving a famous, well-known line from the story.
An illusion that comes from Jewish mythology and deals with God is the story of Lilith's Cave. According to mythology, when God first made man and woman, he made Adam and Lilith. Adam wanted to govern Lilith, and she rebelled, leaving Adam and taking residence with the demons. She told the angel that God sent to get her that she was going to kill all the children. The entrance to the gas chambers was called "Lilith's Cave" in the book as an allusion to this myth. God then made Eve for Adam. Fayge tells Hannah,
"Your words will fly up to heaven and call down the Angel of Death, Lilith's bridegroom, with his poisoned sword." (pg 67)
When Reuven is taken to the gas chamber, Hannah gets upset and feels that all humans are monsters for letting the Holocaust happen, Rivka tells her,
"God is letting it happen....But there is a reason. We cannot see it yet. Like the binding of Issac." (pg 142)
This is a Biblical allusion to the story of Abraham and Issac. God told Abraham to sacrifice his only son to him, and Abraham went as far as binding his son to the sacrificial altar until an Angel of God stops him. God had a reason for his request, and Rivka believes that God has a reason for what is happening to them. Rivka also says,
"You want to be a hero, like Joshua at Jericho, like Samson against the Philistines." (pg 142)
Again, these are Biblical allusions. Joshua, following God's orders, destroyed the city of Jericho and led his people into the Promised Land. Samson, to whom God had given unbelievable strength, was betrayed by Delilah and captured by the Philistines, who cut out his eyes and made him work for them. He pulled down the pillars around the Philistines, killing them and himself.
Finally, there is an allusion to a Yiddish proverb. I do not know what it means, but it says,
"Afile brenen un bruin.... even if you should be burned and roasted. Here that is not a proverb to be spoken aloud." (pg 143)