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COMBINATORICS
2006
14 years 9 months ago
2006
Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and th...
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COMBINATORICS
2006
14 years 9 months ago
2006
The rules of "Bulgarian solitaire" are considered as an operation on the set of partitions to induce a finite dynamical system. We focus on partitions with no preimage u...
COMBINATORICS
2006
14 years 9 months ago
2006
We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show for that for a large class of abelian groups, including the integers ...
COMBINATORICS
2006
14 years 9 months ago
2006
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. The matching number of G is the maximum cardinality of a matching of G. A set S o...
COMBINATORICS
2006
14 years 9 months ago
2006
Abstract. Let G denote a directed graph with adjacency matrix Q and indegree matrix D. We consider the Kirchhoff matrix L = D - Q, sometimes referred to as the directed Laplacian. ...