In William Faulkner's "A Rose for Emily," the depth of conflict does not rest simply between characters. In fact, there are several kinds of conflict in the story.
The first and most obvious conflict is man vs. society. Miss Emily, as the story begins, refuses to pay her taxes.
"See Colonel Sartoris. I have no taxes in Jefferson."
"But, Miss Emily—"
"See Colonel Sartoris...I have no taxes in Jefferson.
We learn also, that when Miss Emily's father dies, she defies the conventions of society at first in refusing to let them take her father's body, insisting he was not dead. When female members of her family come to stay with her—perhaps act as companions or chaperones—she sends them packing. Later she is seen out riding with a Yankee, Homer Baron, a working man from the North.
...the ladies all said, "Of course a Grierson would not think seriously of a Northerner, a day laborer."
Tongues wag, but Emily pays no attention. This shows the conflict still in place at that time between the North and the South, between the upper-class (the landed gentry) and the lower, working class. The comments by the women in time reflect older societal expectations that had been in place for hundreds of years.
Man vs. man was seen in that Emily's father turned away every young man who came to call on his daughter, believing none of them were good enough.
Man vs. man is also obvious when the dead body of Homer Baron is found in a room downstairs. When the facts are compiled, it seems that Miss Emily used rat poisoned she had purchased (from the "druggist") to keep Homer from leaving her.
Another deeper conflict can be seen in the changing of the ways of the Old South in the face of progress. Colonel Sartoris had excused Miss Emily's taxes, which the new aldermen were not happy about. The agreement had been carried out in an "old-fashioned" manner: by way of an oral agreement, rather than by contract. There was no substantiating paperwork. And the fact that Miss Emily went out riding with Homer Baron unchaperoned showed a new sense of independence in this new generation.
The deepest sense of the change in generations can be seen in how Jefferson saw Miss Emily—she was a relic of a time long-gone:
...Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the down.
The men went to her funeral...
...through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house...
Faulkner speaks to the conflicts between men and women, between the individual with society, and even society's loss of respect for the "old ways," as well as a turning away from tradition to embrace a new age.