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On k-homogeneous posets and graphs
1991
Journal of combinatorial theory. Series A
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We show that if a countable poset (52, < ) is l-and 4-homogeneous, then it is k-homogeneous for each k E N. ...
We also show that for every k E fV there are continuousiy many countable &categorical universal graphs which are k-homogeneous but not (k+ l)homogeneous; this answers a question of R. ...
Here we examine the extent to which k-homogeneity implies (k + l)-homogeneity or (k + l)transitivity, particularly for infinite posets and graphs. ...
doi:10.1016/0097-3165(91)90018-c
fatcat:dozvkvszc5fitpfrfio5o2xnye
Page 05 of Mathematical Reviews Vol. , Issue 88b
[page]
1988
Mathematical Reviews
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If a # b and there is an ele- ment c < a,b, then a,b xk for every k € mub{a, b}. Theorem 4: A finite modular 0, 1-poset is algebraically semimodular. ...
More precisely, for every regular cardinal x and regular cardinals u,v <k, there are precisely 2" doubly homogeneous chains whose
05 COMBINATORICS 672
points have character (u,v) (the lengths of minimal ...
On polymorphism-homogeneous relational structures and their clones
2014
Algebra Universalis
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2013 pre-print arXiv:1305.1159v1 fatcat:mtvaxpu22bhhpi2pubyzelcjtiOther Versions
Eventually, we completely characterize the countable polymorphism-homogeneous graphs, the polymorphism-homogeneous posets of arbitrary size, and the countable polymorphism-homogeneous strict posets. ...
We study polymorphism-homogeneity from a model-theoretic, an algebraic, and a combinatorial point of view. ...
Let A be a countable set and let L be a meet-complete sublattice of E(A). Then L is polymorphism-homogeneous if and only if it is arithmetical. ...
doi:10.1007/s00012-014-0310-3
fatcat:mx6av4chwjgupaoxxum5wzdqri
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
[article]
2012
arXiv
pre-print
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In this paper, we compute universal minimal flows of groups of automorphisms of uncountable ω-homogeneous graphs, K_n-free graphs, hypergraphs, partially ordered sets, and their extensions with an ω-homogeneous ...
suggesting the present construction of ωhomogeneous structures. ...
I am also grateful to Lionel Nguyen Van Thé for careful reading and valuable suggestions. ...
arXiv:1204.0037v2
fatcat:vqbtrz5utfegvdyq63zcjs55qm
Hereditary properties of combinatorial structures: posets and oriented graphs
[article]
2007
arXiv
pre-print
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posets and oriented graphs. ...
We also show that there is an initial jump in the possible unlabelled speeds of hereditary properties of posets, tournaments and directed graphs, from bounded to linear speed, and give a sharp lower bound ...
graphs of maximum degree at most one, and the property R consisting of all posets with comparability graphs of minimum degree n − 1. ...
arXiv:math/0702350v1
fatcat:datqccap2nf33gowakfcyprytq
Page 1570 of Mathematical Reviews Vol. , Issue 2002C
[page]
2002
Mathematical Reviews
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Under the mild technical assumption that a, 4 0 and a, = 0, the authors show that the tight graphs are precisely the 1-homogeneous distance-regular graphs. ...
of k-chains [resp. antichains], then the sequences (A;,A2,...) amd (A;,A2,...) are weakly de- creasing and form conjugate partitions of the number N = | P|, it follows that to every finite poset P a ( ...
Finite Homomorphism-Homogeneous Permutations via Edge Colourings of Chains
2012
Electronic Journal of Combinatorics
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In this note, we characterise all permutations on a finite set enjoying this property. ...
with loops) whose non-loop edges are coloured in two colours, thereby 'splitting' the linear order into two posets. ...
So, in fact, we have a colouring of the non-loop edges of the graph of (A, ≤ 1 ) into two colours: blue and red, such that each coloured component induces a poset on A. ...
doi:10.37236/2271
fatcat:gru737avtrgznhemoc7z2tvfgm
Page 5063 of Mathematical Reviews Vol. , Issue 88j
[page]
1988
Mathematical Reviews
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Let k be a field and R a homogeneous k-algebra. Let Q C Rj, the second direct summand of R, be a finite poset. ...
The author characterizes all trees (rank one connected posets without cycles) which are integral over an infinite field k. Michael E. ...
Page 6103 of Mathematical Reviews Vol. , Issue 2001I
[page]
2001
Mathematical Reviews
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Earlier work of Bezrukov on Macaulay posets led to considering products of spider posets Q(k,1) consisting of k + 1 incomparable chains of size / and an extra element that lies above them all. ...
West (1-IL; Urbana, IL)
2001i:06005 06A12 20B27
Droste, Manfred (D-TUD-AL; Dresden);
Kuske, Dietrich (D-TUD-AL; Dresden) ;
Truss, John K. (4-LEED-PMS; Leeds)
On homogeneous semilattices and their automorphism ...
Duality of graded graphs through operads
[article]
2020
arXiv
pre-print
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This pair of graphs is dual for a new notion of duality called ϕ-diagonal duality, similar to the ones introduced by Fomin. ...
We also provide a general way to build pairs of graded graphs from operads, wherein underlying posets are analogs to the Young lattice. ...
Due to the fact that G is combinatorial and K G is a graded space decomposing as K G = ∈N K G( ) (1.1.7) with finite dimensional homogeneous components K G( ) , 0, the space K G can be identified with ...
arXiv:2004.12230v1
fatcat:73olaixwhzdqtjdl4hqdrij3jm
Ramsey classes of topological and metric spaces
2006
Annals of Pure and Applied Logic
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This relates the classification programme for countable homogeneous structures (of Lachlan and Cherlin) to the proof techniques of the structural Ramsey theory. ...
Here we consider the classes of topological and metric spaces which recently were studied in the context of extremally amenable groups and of the Urysohn space. ...
Petersburg meeting, and Professor Anatoly Vershik in particular, for a very nice meeting and hospitality. I also thank Andreas Blass and Aleš Pultr for several remarks related to this paper. ...
doi:10.1016/j.apal.2005.07.004
fatcat:zbnia2gxabanvbq75rngmhlyhi
Page 1735 of Mathematical Reviews Vol. , Issue 87d
[page]
1987
Mathematical Reviews
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The proof is based on the fact that the existence of a 6-central element in every height-one poset is equivalent to a certain prop- erty of bipartite graphs. ...
Finally, as a consequence of these detailed studies, the author is able to show that, although k-transitivity is indeed weaker than k-homogeneity for finite k, w-transitivity and w-homogeneity are equivalent ...
A new operation on partially ordered sets
[article]
2012
arXiv
pre-print
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As an corollary of our results on rotations of finite posets, we obtain that the group of rotating permutations of the random poset is the automorphism group of a homogeneous structure in a finite language ...
In this paper we introduce rotations for finite posets, which can be seen as the poset counterpart of Seidel-switch for finite graphs. ...
Moreover, if A is finite, and a 1 , . . . , a k ∈ A enumerate A in such a way that a j < a i for all 1 ≤ i < j ≤ k, then (3) C A = C a k C a k−1 · · · C a 2 C a 1 . Proof. ...
arXiv:1208.3504v3
fatcat:mekcigdlojgztl2j3guos4yuem
Page 666 of Mathematical Reviews Vol. , Issue 89B
[page]
1989
Mathematical Reviews
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A rooted graph (G, x) is a rooted subgraph of a rooted graph (F, y) if there exists a one-to-one function /:V(G) — V(F) that satisfies (1) [u,v] € E(G) >[f(u), f(v)] € E(F), and (2) f(x) = y. ...
The rotation number /(G, x) of the p-vertex rooted graph (G, x) is defined to be the smallest number q(F) of edges in a p-vertex graph F such that (G, x) is a homogeneous rooted subgraph of F. ...
A new operation on partially ordered sets
2013
Journal of combinatorial theory. Series A
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The file type is application/pdf.
As an corollary of our results on rotations of finite posets, we obtain that the group of rotating permutations of the random poset is the automorphism group of a homogeneous structure in a finite language ...
In this paper we introduce rotations for finite posets, which can be seen as the poset counterpart of Seidel-switch for finite graphs. ...
Moreover, if A is finite, and a 1 , . . . , a k ∈ A enumerate A in such a way that a j < a i for all 1 ≤ i < j ≤ k, then (3) C A = C a k C a k−1 · · · C a 2 C a 1 . Proof. ...
doi:10.1016/j.jcta.2013.04.003
fatcat:e245iblv3fbnfcmv72h6voz4gq
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