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.
Kim, The number of partially ordered sets, Journal of Combinatorial Theory B, 13(3), 276–289 (1972)
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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.