[A] person can be treated as a partner, and consequently exposed to personal liability for the corporation's debts, when representations are made that the enterprise is a partnership and the person is a partner. The representations must be made by the purported partner or with the purported partner's consent. . . . "If the representation is privately made, it may be taken advantage of only by persons to whom it was made; if it was publicly made, anyone (roughly speaking) can make use of it."
. . . . When a representation is private, the statute explicitly requires the claimant to establish that it "has on the faith of such representation, given credit to the actual partnership."