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.

1, 2, 106, 5976, 387564, 27247446, 2020632046, 155622020610, 12327937844924, 998103225615208

Offset: 0

Author

Manda Riehl, Jul 29 2015

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• M. Paukner, L. Pepin, M. Riehl, and J. Wieser, Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080 [math.CO], 2015.
• Manda Riehl, A 321-avoiding diamond with associated permutation 1234.

Crossrefs

Cf. A260331, A260332.