<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Let <italic>J</italic> ⊂ <italic>I</italic> be two monomial ideals such that <italic>I/J</italic> is Cohen Macaulay. By associating a finite posets 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2014-0027_i1.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>I</mi><mo>/</mo><mi>J</mi></mrow><mi>g</mi></msubsup></math><tex-math>$P_{I/J}^g$</tex-math></alternatives></inline-formula>
 to <italic>I/J</italic>, we show that if <italic>I/J</italic> is a Stanley ideal then 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2014-0027_i2.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mrow><mi>I</mi><mo>/</mo><mi>J</mi></mrow><mo stretchy="true">˜</mo></mover></math><tex-math>$\widetilde{I/J}$</tex-math></alternatives></inline-formula>
is also a Stanley ideal, where 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2014-0027_i3.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mrow><mi>I</mi><mo>/</mo><mi>J</mi></mrow><mo stretchy="true">˜</mo></mover></math><tex-math>$\widetilde{I/J}$</tex-math></alternatives></inline-formula>
 is the polarization of <italic>I/J</italic>. We also give relations between sdepth and fdepth of <italic>I/J</italic> and 
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2014-0027_i4.jpg"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mrow><mi>I</mi><mo>/</mo><mi>J</mi></mrow><mo stretchy="true">˜</mo></mover></math><tex-math>$\widetilde{I/J}$</tex-math></alternatives></inline-formula></p></abstract>

Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets 
PI/Jg$P_{I/J}^g$
 to I/J, we show that if I/J is a Stanley ideal then 
I/J˜$\widetilde{I/J}$
is also a Stanley ideal, where 
I/J˜$\widetilde{I/J}$
 is the polarization of I/J. We also give relations between sdepth and fdepth of I/J and 
I/J˜$\widetilde{I/J}$

On Characteristic Poset and Stanley Decomposition

Department of Mathematics, COMSATS Institute of Information Technology, M. A. Jinnah Campus, Raiwand Road, Lahore, Pakistan.

Department of Mathematics, The Abdus Salam International Center of Theocratical Physics, Trieste, Italy.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On Characteristic Poset and Stanley Decomposition"}

Let J ⊂ I be two monomial ideals such that I/J is Cohen Macaulay. By associating a finite posets 
PI/Jg$P_{I/J}^g$
 to I/J, we show that if I/J is a Stanley...

On Characteristic Poset and Stanley Decomposition

Publié en ligne: 20 oct. 2015

Pages: 21 - 28

Reçu: 01 déc. 2012

Accepté: 01 avr. 2013

DOI: https://doi.org/10.2478/auom-2014-0027

Mots clés
monomial ideals, posets, Stanley’s conjecture, Stanley ideals, polarization

© 2014 Sarfraz Ahmad et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Characteristic Poset and Stanley Decomposition

Publié en ligne: 20 oct. 2015

Pages: 21 - 28

Reçu: 01 déc. 2012

Accepté: 01 avr. 2013

DOI: https://doi.org/10.2478/auom-2014-0027

Mots clésmonomial ideals, posets, Stanley’s conjecture, Stanley ideals, polarization

© 2014 Sarfraz Ahmad et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
monomial ideals, posets, Stanley’s conjecture, Stanley ideals, polarization