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A260579 Labelings of n diamond-shaped posets with 4 vertices per diamond where the labels follow the poset relations whose associated reading permutation avoids 321 in the classical sense. 3
1, 2, 106, 5976, 387564, 27247446, 2020632046, 155622020610, 12327937844924, 998103225615208 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
By diamond-shaped poset with 4 vertices, we mean a poset on four elements with e_1 < e_2, e_1 < e_3, e_2 < e_4, e_3 < e_4, and no order relations between e_2 and e_3. In the Hasse diagram for such a poset, we have a least element, two elements in the level above, and one element in the top level, so the diagram resembles a diamond. The associated permutation is the permutation obtained by reading the labels of each poset by levels left to right, starting with the least element.
Additional terms were provided by David Bevan.
LINKS
M. Paukner, L. Pepin, M. Riehl, and J. Wieser, Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080 [math.CO], 2015.
EXAMPLE
For a single diamond (n=1) poset with 4 vertices, we must label the least element 1 and the greatest element 4, and the two central elements can be labeled either 2, 3 or 3, 2 respectively. Thus the associated permutations are 1234 and 1324.
CROSSREFS
Sequence in context: A229016 A222840 A356723 * A125593 A352496 A139887
KEYWORD
nonn,more
AUTHOR
Manda Riehl, Jul 29 2015
STATUS
approved

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Last modified March 29 08:51 EDT 2024. Contains 371268 sequences. (Running on oeis4.)