Does the endomorphism poset determine whether a finite poset is connected? An issue Duffus raised in 1978
Mathematica Bohemica (2023)
- Volume: 148, Issue: 4, page 435-446
- ISSN: 0862-7959
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topFarley, Jonathan David. "Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978." Mathematica Bohemica 148.4 (2023): 435-446. <http://eudml.org/doc/299483>.
@article{Farley2023,
abstract = {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 $P\cong Q$.},
author = {Farley, Jonathan David},
journal = {Mathematica Bohemica},
keywords = {(partially) ordered set; exponentiation; connected},
language = {eng},
number = {4},
pages = {435-446},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978},
url = {http://eudml.org/doc/299483},
volume = {148},
year = {2023},
}
TY - JOUR
AU - Farley, Jonathan David
TI - Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 435
EP - 446
AB - 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 $P\cong Q$.
LA - eng
KW - (partially) ordered set; exponentiation; connected
UR - http://eudml.org/doc/299483
ER -
References
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