When President Carter asked his visitor last Tuesday if China will ease its rules on emigration in the interest of human rights, Vice Premier Teng Hsiao-ping was ready with an anser. If Carter is willing, he said, the most populous nation on Earth can open its exit door just a crack and "send you 10 million immigrants right away."

Carter, who presides over a U.S. immigration quota of 20,000 Chinese yearly from Taiwan, the mainland and all other places, quickly declined Teng's offer. From then on, little was heard from the American side about Chinese exit permits.

As this incident illustrates, Peking's powerful and pint-sized leader in a week on American soil has proven to be a master of political positioning. On a host of delicate subjects, including Soviet "hegemony" and the rean peninsula, Teng's skillful tactics have left the United States as the party to do the adjusting.

The most difficult and weighty matter involves U.S.-Soviet-China triangular relations. The Carter administration is attempting to conclude a strategic arms limitation treaty (SALT) with Moscow and revive detente, while simultaneously establishing full diplomatic relations and cementing closer political and economic ties with the People's Republic of China.

As Teng has made clear in a series of tough anti-Soviet speeches and press statements, China is seeking to improve its relations with Washington at Moscow's expense. The Chinese leader has called for a broad anti-Soviet alliance including the United States, Japan, western Europe and some Third-World states, which is incompatible with Carter's goal of triangular East-West balance. Teng's remarks tend to deepen U.S. public antipathy toward Moscow and thus to sharpen U.S.-Soviet relations.

Carter discomfited the Soviets by saying nothing to refute Teng's stand, though he made it clear publicly that he doesn't completely agree with the Chinese leader on everything. It was only Thursday morning with the issuance of a Sino-American "joint press communique," however, that Carter took an overt step that seemed to side with Peking in the quarrel with Moscow.

Original U.S. plans for the Teng visit included a formal communique after the White House talks, but the Chinese leader told American officials shortly after arriving last Sunday night that he preferred not to have one. Over dinner at the home of Zbigniew Brzezinski, the presidential national security affairs adviser, Teng sia China does not customarily issue communiques on visits abroad. And anyway, he wanted to spend his time in direct and substantive talks rather than in haggling over diplomatic language.

This left the American side to suggest that some less-than-formal statement would be needed, lest the world draw the conclusing that the talks with Carter had been a failure. Teng took a noncommittal position, according to informed sources, saying this would be all right with him, so long as the United States drafted something he could readily approve.

This put the onus on the American side to come up with an acceptable statement, and that in turn argued strongly for the mention of "hegemony," the Chinese code word for Soviet domination.

The concept and the word are very old ones in Chinese, going back to Chou Dynasty (1100 to 400 B.C.) idea of a state without virtue that seeks to destroy legitimate authority. Since Henry A. Kissinger first suggested that it be included in the 1972 Shanghai Communique, China has insisted on it in major statements with foreign governments.

Peking-Tokyo negotiations over a peace and friendship treaty were deadlocked for three years over this single word, until the Japanese finally accepted it with softening language added elsewhere. Presidnet Carter, after negotiations with Peking, used the word in last December's announcement of the establishment of Sino-American dpilomatic relations.

According to official sources, Brzezinski gave the impetus for inclusion of "hegemony" in last Thursday's "joint press communique" (as the less-than-formal statement eventually was called). Brzezinski argued that there was nothing new in this, since the word had been used twice before. Nevertheless, it was certain that the Reussians would see it as a "tilt" toward China, and object on those grounds.

Secretary of State Cyrus R. Vance and Assistant Secretary of State for East Asian and Pacific Affairs Richard Holbrooke were involved in the drafting of the "joint press communique," although it is reported that State Department experts on the Soviet Union were not. Informed sources said the use of the politically radioactive word "hegemony" was not another Brzezinski-Vance bone of contention. Especially under the circumstances, no joint statement with China was likely without it.

The matter of Korea, a strategic and sensitive area where American and Chinese troops fought one another in the early 1950s, appears to have been another case of sophisticated Chinese positioning.

Long before Teng's trip, the Chinese were well aware that Carter would seek their "maximum influence" on North Korea (as Carter said publicly on the eve of Teng's arrival). And the Chinese had no wish to be seen as exerting such U.S.-sponsored pressure on their North Korean ally, even though a reduction of tensions in the divided peninsula is also much in Peking's interest. Following a Jan. 19 overture from South Korean President Park Chung Hee for a new North-South talks, North Korea responded positively -- surprisingly -- on Jan. 23. Since then a back-and-forth series of statements from North and South have raised hopes for a renewal of direct dialogue if not detente on the Korean peninsula.

When the two Koreas suddenly began talking, or at least talking about new talks, shortly before the Teng visit, the U.S. position papers for the Teng visit had to be rewritten. It would make no sense for Carter to urge Teng to pressure the North to do something that already was in process.

The timing of North Korea's recent responses sharply reduced the possibility that relative reasonableness on its part would be seen as a response to Chinese and American pressures. American officials believe, apparently with reason supplied by the Chinese, that some subtle maneuvering on the part of Peking contributed to the recent developments, and thus to defusing the Korean issue at the Carter-Teng discussions.