Ordered sets
BSW Schröder - Springer, 2003 - Springer
Writing the second edition of this text was a wonderful opportunity for a more mature
presentation than I was able to give 13 years ago. The intent still is to give a self-contained …
presentation than I was able to give 13 years ago. The intent still is to give a self-contained …
Powers of partially ordered sets: Cancellation and refinement properties
B Jónsson, R Mckenzie - Mathematica Scandinavica, 1982 - JSTOR
This paper concerns a general operation on partially ordered sets (posets). Given two
posets A and B, AB denotes the set of all order preserving (monotone, isotone) functions …
posets A and B, AB denotes the set of all order preserving (monotone, isotone) functions …
Exponentiation and duality
BA Davey, D Duffus - Ordered Sets: Proceedings of the NATO Advanced …, 1982 - Springer
In a unified treatment of cardinal and ordinal arithmetic G. Birkhoff 18, 20 defined (cardinal)
exponentiation of ordered sets: for ordered sets X and Y, XY (the power) is the set of all …
exponentiation of ordered sets: for ordered sets X and Y, XY (the power) is the set of all …
Arithmetic of finite ordered sets: Cancellation of exponents, II
R McKenzie - Order, 2000 - Springer
Garrett Birkhoff conjectured in 1942 that when A, B, P are finite posets satisfying AP≅ BP,
then A≅ B. We show that this is true. Further, we introduce an operation C (AB), related to …
then A≅ B. We show that this is true. Further, we introduce an operation C (AB), related to …
Powers of ordered sets: Survey Article
D Duffus - Order, 1984 - Springer
Recently there has been significant progress in the study of powers of ordered sets. Much of
this work has concerned cancellation laws for powers and uses these two steps. First …
this work has concerned cancellation laws for powers and uses these two steps. First …
The zig-zag property and exponential cancellation of ordered sets
R McKenzie - Order, 2003 - Springer
This paper outlines a chapter in the theory of ordered sets that concerns decompositions of
ordered sets using various natural operations introduced by Garrett Birkhoff in 1940–chiefly …
ordered sets using various natural operations introduced by Garrett Birkhoff in 1940–chiefly …
Strong G-schemes and strict homomorphisms
F a Campo - arXiv preprint arXiv:1908.06897, 2019 - arxiv.org
Let $\mathfrak {P} _r $ be a representation system of the non-isomorphic finite posets, and
let ${\cal H}(P, Q) $ be the set of order homomorphisms from $ P $ to $ Q $. For finite posets …
let ${\cal H}(P, Q) $ be the set of order homomorphisms from $ P $ to $ Q $. For finite posets …
Arithmetic of finite ordered sets: Cancellation of exponents, I
R McKenzie - Order, 1999 - Springer
Arithmetic of Finite Ordered Sets: Cancellation of Exponents, I Page 1 Order 16: 313–333, 1999.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands. 313 Arithmetic of Finite …
© 2000 Kluwer Academic Publishers. Printed in the Netherlands. 313 Arithmetic of Finite …
[PDF][PDF] About generalized one-to-one mappings between sets of order homomorphisms
F a Campo - arXiv preprint arXiv:1906.11758, 2019 - researchgate.net
Structural properties of finite posets R and S are studied which enforce# H (P, R)≤# H (P, S)
for every finite poset P, where H (P, Q) is the set of order homomorphisms from P to Q. The …
for every finite poset P, where H (P, Q) is the set of order homomorphisms from P to Q. The …
Cancel Culture: The Search for Universally Cancellable Exponents of Posets.
JD Farley - Categories & General Algebraic Structures with …, 2023 - search.ebscohost.com
Abstract Let A, B, C, and D be posets. Assume C and D are finite with a greatest element.
Also assume that A< sup> C</sup>≅= B< sup> D</sup>. Then there exist posets E, X, Y …
Also assume that A< sup> C</sup>≅= B< sup> D</sup>. Then there exist posets E, X, Y …