Abstract
We introduce the partial vine monoid PV n . This monoid is related to the partial transformation semigroup PT n in the same way as the braid group B n is related to the symmetric group S n , and contains both the vine monoid [T.G. Lavers, The theory of vines, Comm. Algebra 25 (4) (1997) 1257–1284] and the inverse braid monoid [D. Easdown, T.G. Lavers, The inverse braid monoid, Adv. Math. 186 (2) (2004) 438–455]. We give a presentation for PV n in terms of generators and relations, as well as a faithful representation in a monoid of endomorphisms of a free group. We also derive a new presentation for PT n .
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