Abstract. We introduce and study the partial singular braid monoid $PSB _n$, a monoid that contains both the inverse braid monoid $IB _n$ and the singular braid monoid $SB _n$. Our main results include a characterization of Green's relations, a presentation in terms of generators and relations, and a proof that $PSB _n$ embeds in the semigroup algebra $CIB_n $.

DOI: 10.14232/actasm-014-012-7

AMS Subject Classification (1991): 20F36; 20M05

Keyword(s): braid groups, singular braid monoids, inverse braid monoids, presentations, Birman's conjecture

Received January 29, 2014, and in revised from May 8, 2014. (Registered under 12/2014.)