FOR NINE WEEKS, the Yale University administration and the union representing the school's dining hall and maintenance workers have faced each other in a contract stalemate that still seems as far from settlement as it did when it first began. Until last week, the two sides had not met to discuss a new pact since negotiations broke off on September 30. And after only a few hours of discussion last Tuesday, the negotiators called it quite once again, because neither the university nor the union appeared willing to compromise on its original position.

Local 35 of the Federation of University Employees, AFL-CIO, says the workers want to compromise, and adds that all of its bargaining positions are negotiable. But first, union officials say, Yale must make some concessions--yet the university administrators have maintained since even before the strike began that their current proposals are final. As a result, the longer the strike lasts, the more entrenched the two sides become. In statements to the press and handouts distributed at Yale, both sides have stuck to their guns so firmly that now the central issue of the strike is no longer wage increases or job security arrangements. Instead, the act of negotiating, and especially the question of submitting the dispute to third-party arbitration, have become the key points in the debate.

Vincent J. Sirbella, the union's business manager and the leader of the strike, has repeatedly asked the university to agree to some form of arbitration.

But Yale officials have rejected such a solution, arguing that an arbitrator would tend to "split the difference" between the two sides, rather than seek a fair settlement. In addition, says Donald M. Stevens, director of employee relations at Yale, even if the university agrees only to non-binding arbitration, it would be "almost impossible" for it to reject such a settlement without being accused of prolonging the strike.

The Yale administration has good reason to try to avoid an arbitrated settlement. In 1974, after two months of a strike by Local 35, the university agreed to "non-binding fact-finding" by an outside arbitrator, who decided in favor of the union's proposals, which included a 7-per-cent wage increase. Kingman Brewster, then Yale's President, accepted all the proposals, but administrators say now they believe the university was pressured into signing the contract. So this time around, Yale is playing the game of collective bargaining more carefully. Far from announcing any willingness to accept arbitration again, university officials say instead that it would have been irresponsible of them to have played games with the negotiations, keeping their final offer secret until arbitration might begin.

University officials, however, have not had much luck in convincing Yale students and faculty that non-binding arbitration would be a mistake; about 2400 members of the University community have signed petitions urging the administration to accept arbitration. Yet so far the only persons from outside the university involved in the negotiations have been federal and Connecticut state mediators, who act mostly as go-betweens when the two sides meet.

Negotiations for this year's contract began last May, two months before the union's old agreement was due to expire. Local 35 is asking for a one-year contract with an 8-per-cent wage increase, while the university has proposed a package of a wage increase and partial cost-of-living adjustment that, it says, would raise wages from 16 to 22 per cent over three years, depending on the employee's job status. But union leaders charge that Yale's figures are misleading and partially false. Under the university's proposal, they say, the real wages paid to most workers would fall if the current rate of inflation remains constant. University officials respond by citing the results of a survey, taken last spring, of wage rates offered by other colleges and universities in the northeast, including Harvard. The survey found that Yale's wages were on the average 25 per cent higher than those offered for similar jobs.

The second major area of disagreement between the two sides concerns Yale's policy of replacing retired workers with part-time employees--many of them students--who do not receive fringe benefits if they work fewer than 20 hours a week. Since 1971 Yale has replaced about 400 full-time positions with part-time workers. As a result of the decrease in benefits, the union says the average standard of living of Local 35 members has declined. Moreover, over half the union's 1400 members are now students or other part-timers who do not have a full-time stake in the union, and are probably less likely to support its demands.

Yale officials insist they must keep the option of hiring more part-timers, to provide the most efficient services. Although the union has asked for a number of broad assurances that Yale will not continue to cut down on its full-time employees, the university has offered only a guarantee that it will not reduce the work-hours of current full-timers--unless there is a major change such as "reduction or discontinuation of services or a technological change." And to union members, that caveat threatens their job security.

Yale officials justify the reduction in work hours by saying that in the dining halls, part-time workers are often more productive than full-time employees. But the real reason the university wants to keep open its option to hire part-timers is financial: following a $6 million budget deficit last year, administrators claim Yale must now hold the line on costs. And of course, hiring more full-time workers would simply cost more.

Union officials, however, charge that the university's financial position is not as bad as it has been made out to be. In a paper prepared for Local 35, Richard D. Wolff, associate professor of economics at the University of Massachuetts, states that last year's Yale deficit resulted largely from temporary expenses, such as increased fuel costs during last year's unusually cold winter. In addition, Wolff writes that the Yale Corporation created much of Yale's current financial problem itself last January, when it decided to freeze the amount of the school's endowment the administration can devote to general expenses.

YALE OFFICIALS countered Wolff's report with a stream of statements and handouts supporting the university's positions, and over the weeks the dispute has bogged down into a stalemate over the facts and figures of each side's arguments. Meanwhile, the strikers are living on a $30-a-week union picketers' allowance, as white collar workers man the facilities that are still open. The university's power plants and the freshman commons dining hall remain in use, but the residential college dining halls and the custodial service have been shut down since the strike began. The university is giving students $5.65 a day for meals, and although they may eat in the commons, most have avoided union picket lines there by cooking in their rooms--which is officially verboten--or eating out.

Among students, support for the union seems to be growing; a rally last month in support of non-binding arbitration drew more than 400 students and workers, and last week more than 30 students were arrested when they and a group of strikers attempted to block a fuel oil truck from delivering to a power plant. But the students are not the ones who will decide when the strike will end. The university and the union have both said they are willing to hold out for as long as the strike lasts. But eventually there will have to be some sort of compromise.

The issues involved in the dispute are intricate, and the facts each side cites to support their positions often contradict one another. An outside hand is clearly needed to guide the negotiators, to provide students and other members of the Yale community with an objective view of the issues. If university officials and union leaders are confident that their positions are just, there is no reason for them to fear the judgment of an impartial arbitrator. Both sides will probably not, of course, end up with a settlement with which they are completely happy. Yet with the strike over, Yale can get back to the business of education, and everyone should come out a winner.