The Betti numbers of forests
classification
🧮 math.AC
math.CO
keywords
forestsidealsbettiinvariantnumbersassociatedcertaincombinatorial
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This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs.
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