A matrix-extension method generates naturally labeled posets by characterizing valid extensions as order ideals satisfying vA = v, with applications to sieve algorithms and Burnside enumeration via automorphism groups.
Day, Characterizations of finite lattices that are bounded-homomorphic images of sub- lattices of free lattices, Canadian Journal of Mathematics, 31(1), 69–78 (1979)
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Generating naturally labeled posets through matrix extensions, order ideals and automorphism groups
A matrix-extension method generates naturally labeled posets by characterizing valid extensions as order ideals satisfying vA = v, with applications to sieve algorithms and Burnside enumeration via automorphism groups.