"The town had just let the contracts for paving the sidewalks, and in the summer after her father’s death they began the work. The construction company came with riggers and mules and machinery, and a foreman named Homer Barron, a Yankee--a big, dark, ready man, with a big voice and eyes lighter than his face...Presently we began to see him and Miss Emily on Sunday afternoons driving in the yellow-wheeled buggy and the matched team of bays from the livery stable."

This excerpt means that the town had sent out bids and had hired a company to pour concrete for the new sidewalks.  The riggers are trained to build the forms for the sidewalks. The mules and machinery are what the riggers work with.  These men are the men who will work to build the new sidewalks and Homer was the foreman.

The story indicates that Homer liked to spend his evenings in the company of younger men at the Elks Lodge. There is gossip in the town about Homer being form the north and his lifestyle.  However, I did not get the impression that he was a homosexual.  He did not want to be tied down.  He was not the marrying type of man and did not want to give up his free wheeling lifestyle.