منابع مشابه
Rank Functions on Rooted Tree Quivers
The free abelian group R(Q) on the set of indecomposable representations of a quiver Q, over a field K, has a ring structure where the multiplication is given by the tensor product. We show that if Q is a rooted tree (an oriented tree with a unique sink), then the ring R(Q)red is a finitely generated Z-module (here R(Q)red is the ring R(Q) modulo the ideal of all nilpotent elements). We will de...
متن کاملRank functors and representation rings of quivers
To my wife Kelly. ii ACKNOWLEDGEMENTS I would like to thank, first and foremost, my advisor Harm Derksen for guiding me along the path to becoming a mathematical researcher. The many hours we spent in discussion and his creative suggestions were absolutely essential for completion of this project. I would also like to thank John Stembridge for reading this dissertation and for some helpful disc...
متن کاملExpected rank and randomness in rooted graphs
For a rooted graph G, let EVb(G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We determine the expected value of EVb(G; p) for random trees, and include a connection to unrooted trees. We also consider rooted digraphs, computing the expected value of a random orientation of a rooted graph G in terms of E...
متن کاملExtremal functions for rooted minors
The graph G contains a graph H as a minor if there exist pair-wise disjoint sets {Si ⊆ V (G)|i = 1, . . . , |V (H)|} such that for every i, G[Si] is a connected subgraph and for every edge uv in H, there exists an edge of G with one end in Su and the other end in Sv. A rooted H minor in G is a minor where each Si of minor contains a predetermined xi ∈ V (G). We prove that if the constant c is s...
متن کاملColoring Rooted Subtrees on Abounded Degree Host Tree
We consider a rooted tree R to be a rooted subtree of a given tree T if the tree obtained by replacing the directed arcs of R by undirected edges is a subtree of T . In this work, we study the problem of assigning colors to a given set of rooted subtrees R of a given host tree T such that if any two rooted subtrees share a directed edge, then they are assigned different colors. The objective is...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2010
ISSN: 0012-7094
DOI: 10.1215/00127094-2010-006