CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 03C15 ( Denumerable structures )

  Expand all        Collapse all Results 1 - 2 of 2

1. CMB Online first

Sokić, Miodrag
Indicators, chains, antichains, Ramsey property
We introduce two Ramsey classes of finite relational structures. The first class contains finite structures of the form $(A,(I_{i})_{i=1}^{n},\leq ,(\preceq _{i})_{i=1}^{n})$ where $\leq $ is a total ordering on $A$ and $% \preceq _{i}$ is a linear ordering on the set $\{a\in A:I_{i}(a)\}$. The second class contains structures of the form $(A,\leq ,(I_{i})_{i=1}^{n},\preceq )$ where $(A,\leq )$ is a weak ordering and $% \preceq $ is a linear ordering on $A$ such that $A$ is partitioned by $% \{a\in A:I_{i}(a)\}$ into maximal chains in the partial ordering $\leq $ and each $\{a\in A:I_{i}(a)\}$ is an interval with respect to $\preceq $.

Keywords:Ramsey property, linear orderings
Categories:05C55, 03C15, 54H20

2. CMB 2000 (vol 43 pp. 397)

Bonato, Anthony; Cameron, Peter; Delić, Dejan
Tournaments and Orders with the Pigeonhole Property
A binary structure $S$ has the pigeonhole property ($\mathcal{P}$) if every finite partition of $S$ induces a block isomorphic to $S$. We classify all countable tournaments with ($\mathcal{P}$); the class of orders with ($\mathcal{P}$) is completely classified.

Keywords:pigeonhole property, tournament, order
Categories:05C20, 03C15

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/