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Congruence-uniform lattices whose alternate order is a lattice.
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%I #15 Aug 29 2019 16:55:43

%S 1,1,0,1,1,2,3,8,16,41,107,304,891,2735

%N Congruence-uniform lattices whose alternate order is a lattice.

%C A lattice is congruence-uniform if it can be constructed from the singleton-lattice by a sequence of interval doublings. This doubling process gives rise to an alternate way of ordering the lattice elements. See the references for more details.

%H A. Day, <a href="http://dx.doi.org/10.4153/CJM-1979-008-x">Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices</a>, Canadian Journal of Mathematics, 31 (1979), 617-631.

%H H. Mühle, <a href="https://arxiv.org/abs/1708.02104">On the lattice property of shard orders</a>, arXiv:1708.02104 [math.CO], 2017.

%H N. Reading, <a href="http://dx.doi.org/10.1007/978-3-319-44236-5_9">Lattice theory of the poset of regions</a>, Birkhäuser, 2016, pages 465-467.

%Y Cf. A292790, A292852.

%K nonn,more

%O 1,6

%A _Henri Mühle_, Sep 25 2017

%E a(13)-a(14) from _Henri Mühle_, Aug 29 2019