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Title

MONOMIAL IDEALS WITH K-RESOLUTION

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Abstract

 FOR A POSITIVE INTEGER K A CLASS OF MONOMIAL IDEALS, IS CALLED MONOMIAL IDEALS WITH K-RESOLUTION, IS INTRODUCED. IT IS SHOWN THAT THE STANLEY-REISNER IDEAL OF THE ALEXANDER DUAL OF A SIMPLICIAL COMPLEX D HAS A K-RESOLUTION IF AND ONLY IF D IS CM (K), I.E., THE ITH REDUCED HOMOLOGY GROUP OF THE LINK OF F IN D VANISHES UNLESS I = DIM(LINKDF). AS A MAIN RESULT, WE CHARACTERIZE ALL BIPARTITE GRAPHS WHOSE INDEPENDENCE COMPLEXES ARE CM (K). OUR RESULT IMPROVES A RESULT DUE TO HERZOG AND HIBI AND ALSO A RESULT DUE TO VILLARREAL.

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