Hammocks have been considered by Brenner ,
who gave a numerical criterion
for a finite translation quiver to be the Auslander–Reiten quiver
representation-finite algebra. Ringel and Vossieck 
gave a combinatorial definition
of left hammocks which generalised the concept of hammocks in the sense
as a translation quiver H and an additive function h
on H (called the hammock
function) satisfying some conditions. They showed that a thin left hammock
finitely many projective vertices is just the preprojective component of
Auslander–Reiten quiver of the category of [Sscr ]-spaces, where [Sscr ]
is a finite partially ordered set (abbreviated as ‘poset’).
role in the representation theory
of posets is played by two differentiation algorithms. One of the algorithms
developed by Nazarova and Roiter , and it
reduces a poset [Sscr ] with a maximal
element a to a new poset [Sscr ]′=a∂[Sscr ].
The second algorithm was developed by
Zavadskij , and it reduces a poset [Sscr ]
with a suitable pair (a, b) of elements a, b
a new poset [Sscr ]′=∂(a,b)[Sscr ].
The main purpose of this paper is to construct new left
hammocks from a given one, and to show the relationship between these new
hammocks and the Nazarova–Roiter algorithm. In a later paper
, we discuss the
relationship between hammocks and the Zavadskij algorithm.