Details
| Original language | English |
|---|---|
| Pages (from-to) | 247-265 |
| Number of pages | 19 |
| Journal | ORDER |
| Volume | 8 |
| Issue number | 3 |
| Publication status | Published - Sept 1991 |
Abstract
A refinement of an algorithm developed by Culberson and Rawlins yields the numbers of all partially ordered sets (posets) with n points and k antichains for n≤11 and all relevant integers k. Using these numbers in connection with certain formulae derived earlier by the first author, one can now compute the numbers of all quasiordered sets, posets, connected posets etc. with n points for n≤14. Using the well-known one-to-one correspondence between finite quasiordered sets and finite topological spaces, one obtains the numbers of finite topological spaces with n points and k open sets for n≤11 and all k, and then the numbers of all topologies on n≤14 points satisfying various degrees of separation and connectedness properties, respectively. The number of (connected) topologies on 14 points exceeds 1023.
Keywords
- AMS subject classifications (1991): 05A15, 05A19, 06A06, 54-04, antichain, connected, generating function, partially ordered set, Quasiordered set, separation axiom, topology
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
- Computer Science(all)
- Computational Theory and Mathematics
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In: ORDER, Vol. 8, No. 3, 09.1991, p. 247-265.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Counting finite posets and topologies
AU - Erné, Marcel
AU - Stege, Kurt
PY - 1991/9
Y1 - 1991/9
N2 - A refinement of an algorithm developed by Culberson and Rawlins yields the numbers of all partially ordered sets (posets) with n points and k antichains for n≤11 and all relevant integers k. Using these numbers in connection with certain formulae derived earlier by the first author, one can now compute the numbers of all quasiordered sets, posets, connected posets etc. with n points for n≤14. Using the well-known one-to-one correspondence between finite quasiordered sets and finite topological spaces, one obtains the numbers of finite topological spaces with n points and k open sets for n≤11 and all k, and then the numbers of all topologies on n≤14 points satisfying various degrees of separation and connectedness properties, respectively. The number of (connected) topologies on 14 points exceeds 1023.
AB - A refinement of an algorithm developed by Culberson and Rawlins yields the numbers of all partially ordered sets (posets) with n points and k antichains for n≤11 and all relevant integers k. Using these numbers in connection with certain formulae derived earlier by the first author, one can now compute the numbers of all quasiordered sets, posets, connected posets etc. with n points for n≤14. Using the well-known one-to-one correspondence between finite quasiordered sets and finite topological spaces, one obtains the numbers of finite topological spaces with n points and k open sets for n≤11 and all k, and then the numbers of all topologies on n≤14 points satisfying various degrees of separation and connectedness properties, respectively. The number of (connected) topologies on 14 points exceeds 1023.
KW - AMS subject classifications (1991): 05A15, 05A19, 06A06, 54-04
KW - antichain
KW - connected
KW - generating function
KW - partially ordered set
KW - Quasiordered set
KW - separation axiom
KW - topology
UR - http://www.scopus.com/inward/record.url?scp=0040452260&partnerID=8YFLogxK
U2 - 10.1007/BF00383446
DO - 10.1007/BF00383446
M3 - Article
AN - SCOPUS:0040452260
VL - 8
SP - 247
EP - 265
JO - ORDER
JF - ORDER
SN - 0167-8094
IS - 3
ER -