6 research outputs found
Level Eulerian Posets
The notion of level posets is introduced. This class of infinite posets has
the property that between every two adjacent ranks the same bipartite graph
occurs. When the adjacency matrix is indecomposable, we determine the length of
the longest interval one needs to check to verify Eulerianness. Furthermore, we
show that every level Eulerian poset associated to an indecomposable matrix has
even order. A condition for verifying shellability is introduced and is
automated using the algebra of walks. Applying the Skolem--Mahler--Lech
theorem, the -series of a level poset is shown to be a rational
generating function in the non-commutative variables and .
In the case the poset is also Eulerian, the analogous result holds for the
-series. Using coalgebraic techniques a method is developed to
recognize the -series matrix of a level Eulerian poset
Triangulations
The earliest work in topology was often based on explicit combinatorial models – usually triangulations – for the spaces being studied. Although algebraic methods in topology gradually replaced combinatorial ones in the mid-1900s, the emergence of computers later revitalized the study of triangulations. By now there are several distinct mathematical communities actively doing work on different aspects of triangulations. The goal of this workshop was to bring the researchers from these various communities together to stimulate interaction and to benefit from the exchange of ideas and methods
Combinatorics
This is the report on the Oberwolfach workshop on Combinatorics, held 1–7 January 2006. Combinatorics is a branch of mathematics studying families of mainly, but not exclusively, finite or countable structures – discrete objects. The discrete objects considered in the workshop were graphs, set systems, discrete geometries, and matrices. The programme consisted of 15 invited lectures, 18 contributed talks, and a problem session focusing on recent developments in graph theory, coding theory, discrete geometry, extremal combinatorics, Ramsey theory, theoretical computer science, and probabilistic combinatorics