Abstract:We define a total order, which we call rooted order, on minimal generating set of J(P n ) s where J(P n ) is the cover ideal of a path graph on n vertices. We show that each power of a cover ideal of a path has linear quotients with respect to the rooted order. Along the way, we characterize minimal generating set of J(P n ) s for s ≥ 3 in terms of minimal generating set of J(P n ) 2 . We also discuss the extension of the concept of rooted order to chordal graphs. Computational examples suggest that such order… Show more
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