Abstract
Motivated by a relation of the 1-constrained Kadomtsev - Petviashvili (KP) hierarchy with the 2-component KP hierarchy, the tau-functions of the vector k-constrained KP hierarchy are constructed by using an analogue of the Baker - Akhiezer (m + 1)-point function. These tau-functions are expressed in terms of Wronskian-type determinants.
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