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We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial ideal correspond to the maximal faces (the facets) of a simplicial complex ∆. This correspondence gives us a new method, distinct from the Stanley-Reisner correspondence,… (More)

- Christopher A. Francisco, Huy Tài Hà
- J. Comb. Theory, Ser. A
- 2008

Let G be a simple (i.e., no loops and no multiple edges) graph. We investigate the question of how to modify G combinatorially to obtain a sequentially CohenMacaulay graph. We focus on modifications given by adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex in G. We… (More)

- Christopher A. Francisco, Huy Tài Hà, Adam Van Tuyl
- Discrete Mathematics
- 2010

- Huy Tài Hà, Kuei-Nuan Lin
- SIAM J. Discrete Math.
- 2015

- Steven Dale Cutkosky, Huy Tài Hà, Hema Srinivasan, Emanoil Theodorescu
- 2004

Let k be a field of characteristic 0, R = k[x1, . . . , xd] be a polynomial ring, and m its maximal homogeneous ideal. Let I ⊂ R be a homogeneous ideal in R. Let λ(M) denote the length of an Rmodule M. In this paper, we show that lim n→∞ λ ( H m (R/In) ) nd = lim n→∞ λ ( ExtR ( R/In,R(−d) ) ) nd always exists. This limit has been shown to be e(I)/d!… (More)

- Rachelle R. Bouchat, Huy Tài Hà, Augustine O'Keefe
- J. Comb. Theory, Ser. A
- 2011

- Rachelle R. Bouchat, Huy Tài Hà, Augustine O'Keefe
- J. Comb. Theory, Ser. A
- 2012

- Huy Tài Hà, Duc Hô
- Australasian J. Combinatorics
- 2015

Let G be a simple graph on n vertices. LetH be either the complete graph Km or the complete bipartite graph Kr,s on a subset of the vertices in G. We show that G contains H as a subgraph if and only if βi,α(H) ≤ βi,α(G) for all i ≥ 0 and α ∈ Z. In fact, it suffices to consider only the first syzygy module. In particular, we prove that β1,α(H) ≤ β1,α(G) for… (More)

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