On the tiling by translation problem
Discrete Applied Mathematics
Equations on palindromes and circular words
Theoretical Computer Science
A linear time and space algorithm for detecting path intersection in Zd
Theoretical Computer Science
Two infinite families of polyominoes that tile the plane by translation in two distinct ways
Theoretical Computer Science
A note on a result of daurat and nivat
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
A parallelogram tile fills the plane by translation in at most two distinct ways
Discrete Applied Mathematics
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We study the combinatorial properties and the problem of generating exhaustively double square tiles, i.e. polyominoes yielding two distinct periodic tilings by translated copies such that every polyomino in the tiling is surrounded by exactly four copies. We show in particular that every prime double square tile may be obtained from the unit square by applying successively some invertible operators on double squares. As a consequence, we prove a conjecture of Provencal and Vuillon (2008) [17] stating that these polyominoes are invariant under rotation by angle @p.