  The paper bounds the number of tessellations with T-shaped vertices on a
fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms
retrieve them, proving injectivity. This yields existence of a completely
random T-tessellation, as defined by Ki\^en Ki\^eu et al., and of its Gibbsian
modifications. The combinatorial bound is sharp, but likely pessimistic in
typical cases.
