A note on the edge ideals of Ferrers graphs
نویسنده
چکیده
We determine the arithmetical rank of every edge ideal of a Ferrers graph.
منابع مشابه
Ferrers Graphs and Related Ideals
This abstract is essentially taken from the introduction of the paper Monomial and toric ideals associated to Ferrers graphs [13], written jointly with Alberto Corso. A Ferrers graph is a bipartite graph on two distinct vertex sets X = {x1, . . . , xn} and Y = {y1, . . . , ym} such that if (xi, yj) is an edge of G, then so is (xp, yq) for 1 ≤ p ≤ i and 1 ≤ q ≤ j. In addition, (x1, ym) and (xn, ...
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Each partition λ = (λ1, λ2, . . . , λn) determines a so-called Ferrers tableau or, equivalently, a Ferrers bipartite graph. Its edge ideal, dubbed a Ferrers ideal, is a squarefree monomial ideal that is generated by quadrics. We show that such an ideal has a 2-linear minimal free resolution; i.e. it defines a small subscheme. In fact, we prove that this property characterizes Ferrers graphs amo...
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The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D_1(u,e|G) and D_2(u,e|G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W_{ve_1}(G) and W_{ve_2}(G) were introduced. In this paper, we present exact form...
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We introduce a specialization technique in order to study monomial ideals that are generated in degree two by using our earlier results about Ferrers ideals. It allows us to describe explicitly a cellular minimal free resolution of various ideals including any strongly stable and any squarefree strongly stable ideal whose minimal generators have degree two. In particular, this shows that thresh...
متن کاملAlgebraic Properties of Edge Ideals via Combinatorial Topology
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature regarding linearity, Betti numbers, and (sequentially) Cohen-Macaulay properties of edges ideals associated to chordal, complements of chordal, and Ferrers g...
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تاریخ انتشار 2006