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On k-homogeneous posets and graphs

M Droste, H.D Macpherson
1991 Journal of combinatorial theory. Series A  
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  
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

Christian Pech, Maja Pech
2014 Algebra Universalis  
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]

Dana Bartosova
2012 arXiv   pre-print
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]

József Balogh, Béla Bollobás, Robert Morris
2007 arXiv   pre-print
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  
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

Igor Dolinka, Éva Jungábel
2012 Electronic Journal of Combinatorics  
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  
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  
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]

Samuele Giraudo
2020 arXiv   pre-print
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

Jaroslav Nešetřil
2006 Annals of Pure and Applied Logic  
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  
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]

Péter Pál Pach, Michael Pinsker, András Pongrácz, Csaba Szabó
2012 arXiv   pre-print
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  
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

Péter Pál Pach, Michael Pinsker, András Pongrácz, Csaba Szabó
2013 Journal of combinatorial theory. Series A  
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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