What connections are there between the stories of A Rose for Emily by William Faulkner, The Story of an Hour by Kate Chopin, and Barn Burning by William Faulkner?

ln all three stories, the central character finds freedom from male control. Each of the three characters, however, achieves freedom in a very different way.
In "A Rose for Emily," Emily is initially under the dominion of her father, who chases potential husbands away, forcing her to remain single. After he dies, Emily takes up with Homer Barron. Everybody expects them to marry. However, after Emily's death, the townspeople find she has killed him and kept his decaying corpse with her. This way, she could exert power and control over him as her father once controlled her. Homer, like her father, could not ruin her life. Nor could he leave her:

For a long while we just stood there, looking down at the profound and fleshless grin. The body had apparently once lain in the attitude of an embrace, but now the long sleep that outlasts love, that conquers even the grimace of love, had cuckolded him. What was left of him, rotted beneath what was left of the nightshirt, had become inextricable from the bed in which he lay; and upon him and upon the pillow beside him lay that even coating of the patient and biding dust.
Then we noticed that in the second pillow was the indentation of a head. One of us lifted something from it, and leaning forward, that faint and invisible dust dry and acrid in the nostrils, we saw a long strand of iron-gray hair.

In the shortest of these three stories, Chopin's "A Story of an Hour," the central character, Josephine Mallard, finds freedom in the most passive of ways. When she hears the news that her husband, Richard, has been killed in a railroad accident, she is at first grieved. Later, she finds herself overjoyed to be free of him, even though he had loved her:

"Free! Body and soul free!" she kept whispering.

As she absorbs the reality of his death, she looks forward to no longer having to bend her will to his:

Her fancy was running riot along those days ahead of her. Spring days, and summer days, and all sorts of days that would be her own. She breathed a quick prayer that life might be long. It was only yesterday she had thought with a shudder that life might be long.

When Richard returns and she finds out the news of his death was a mistake, she can't face giving up her newfound freedom even though it has only lasted an hour. That hour has changed her, and she can't go back to her former life. She therefore achieves a different form of freedom—or escape—through dying. Having tasted freedom, she prefers death to its loss. She gains this freedom passively. She does not actively kill herself, Nevertheless, her sudden death liberates her.
In "Barn Burning" Sarty also breaks free of a patriarch. In this case, it is his arsonist father, who beats Sarty when he thinks he is going to betray him as a barn burner. His father expects him to always stand by the family.
However, when Sarty believes his father has died (although he hasn't) in yet another barn burning, he runs away from his family, breaking free from patriarchy's grip:

He began to run, stumbling, tripping ... without ceasing to run, looking backwards over his shoulder at the glare... running among the invisible trees.

In all three cases, the freedom comes at great price. Josephine dies, Emily lives with a corpse, and Sarty runs off without money or protection into the woods to fend for himself. Nevertheless, all three find freedom.
All three stories also use omniscient narration. In both "A Rose for Emily" and "Story of an Hour," this allows the author to surprise the reader: in "A Rose for Emily" we don't expect Emily to be sleeping with her husband's corpse. In "Story of an Hour," we initially believe Josephine is overcome with grief. The revelation that she is happy about it is shocking. "Barn Burning" sticks much closer to telling the story through Sarty's eyes, but there are places where Faulkner inserts a narrative voice that could not be that of a ten year old boy, such as when the narrator comments the following:

There was something about his [Sarty's father's] wolflike independence and even courage when the advantage was at least neutral which impressed strangers, as if they got from his latent ravening ferocity not so much a sense of dependability as a feeling that his ferocious conviction in the rightness of his own actions would be of advantage to all whose interest lay with his.

By using omniscient narration, the authors achieve freedom: the freedom to tell their stories in the most powerful possible way.