NEW YORK — Barington Capital Group, the activist shareholder that is trying to shake things up at Dilliard’s Inc., said in a regulatory filing with the Securities and Exchange Commission that is has asked Dillard’s to provide it with a list of shareholders. The expectation on Wall Street is that Barington and its partner the Clinton Group are preparing to launch a proxy fight to acquire one or two seats on the board. Dillard’s has a dual structure where there are two different types of stock ownership, giving the Dillard’s family control over the retailer and eight of the 12 board seats.