On Characteristic Poset and Stanley Decomposition
On Characteristic Poset and Stanley Decomposition
Abstract Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msubsup> <m:mi>P</m:mi> <m:mrow> <m:mi>I</m:mi> <m:mo>/</m:mo> <m:mi>J</m:mi> </m:mrow> <m:mi>g</m:mi> </m:msubsup> </m:math> $P_{I/J}^g$ to I/J , we show that if I/J is a Stanley ideal then <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> …