A.: Counting partial orders with a fixed number of comparable pairs [2 citations — 0 self]
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by Hans Jurgen Promel, Angelika Steger, Anusch Taraz
Combin. Probab. Comput
http://www.informatik.hu-berlin.de/~proemel/publikationen/PST99.ps.gz
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Abstract:
In 1978, Dhar suggested a model of a lattice gas whose states are partial orders. In this context he raised the question of determining the number of partial orders with a fixed number of comparable pairs. Dhar conjectured that in order to find a good approximation to this number, it should suffice to enumerate families of layer posets. In this paper we prove this conjecture and thereby prepare the ground for a complete answer to the question. 1
Citations
| 17 | Asymptotic enumeration of partial orders on a finite set – Kleitman, Rothschild - 1975 |
| 5 | Asymptotic enumeration of partially ordered sets – Dhar - 1980 |
| 5 | The number of finite topologies – Kleitman, Rothschild - 1970 |
| 5 | Regular partitions of graphs, Probl`emes en Combinatoire et Th'eorie des Graphes – Szemer'edi - 1978 |
| 4 | A.: Phase transitions in the evolution of partial orders – Promel, Steger, et al. - 1999 |
| 3 | Entropy and phase transitions in partially ordered sets – Dhar - 1978 |
| 1 | A phase transition on partial orders – Kleitman, Rothschild - 1979 |
