| Title:
|
Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978 (English) |
| Author:
|
Farley, Jonathan David |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
435-446 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Duffus wrote in his 1978 Ph.D. thesis, ``It is not obvious that $P$ is connected and $P^P\cong Q^Q$ imply that $Q$ is connected'', where $P$ and $Q$ are finite nonempty posets. We show that, indeed, under these hypotheses $Q$ is connected and $P\cong Q$. (English) |
| Keyword:
|
(partially) ordered set |
| Keyword:
|
exponentiation |
| Keyword:
|
connected |
| MSC:
|
06A07 |
| idZBL:
|
Zbl 07790595 |
| idMR:
|
MR4673829 |
| DOI:
|
10.21136/MB.2022.0010-22 |
| . |
| Date available:
|
2023-11-23T12:33:02Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151965 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
