Peak Quasisymmetric Functions and Eulerian Enumeration
Adv. Math. 176: 248--276 (2003) Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of $\cd$-index, long studied in the context of convex polytope...
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| creator | Billera, Louis J Hsiao, Samuel K van Willigenburg, Stephanie |
| description | Adv. Math. 176: 248--276 (2003) Via duality of Hopf algebras, there is a direct association between peak
quasisymmetric functions and enumeration of chains in Eulerian posets. We study
this association explicitly, showing that the notion of $\cd$-index, long
studied in the context of convex polytopes and Eulerian posets, arises as the
dual basis to a natural basis of peak quasisymmetric functions introduced by
Stembridge. Thus Eulerian posets having a nonnegative $\cd$-index (for example,
face lattices of convex polytopes) correspond to peak quasisymmetric functions
having a nonnegative representation in terms of this basis. We diagonalize the
operator that associates the basis of descent sets for all quasisymmetric
functions to that of peak sets for the algebra of peak functions, and study the
$g$-polynomial for Eulerian posets as an algebra homomorphism. |
| doi_str_mv | 10.48550/arxiv.0706.3486 |
| format | Article |
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quasisymmetric functions and enumeration of chains in Eulerian posets. We study
this association explicitly, showing that the notion of $\cd$-index, long
studied in the context of convex polytopes and Eulerian posets, arises as the
dual basis to a natural basis of peak quasisymmetric functions introduced by
Stembridge. Thus Eulerian posets having a nonnegative $\cd$-index (for example,
face lattices of convex polytopes) correspond to peak quasisymmetric functions
having a nonnegative representation in terms of this basis. We diagonalize the
operator that associates the basis of descent sets for all quasisymmetric
functions to that of peak sets for the algebra of peak functions, and study the
$g$-polynomial for Eulerian posets as an algebra homomorphism.</description><identifier>DOI: 10.48550/arxiv.0706.3486</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2007-06</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/0706.3486$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.0706.3486$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Billera, Louis J</creatorcontrib><creatorcontrib>Hsiao, Samuel K</creatorcontrib><creatorcontrib>van Willigenburg, Stephanie</creatorcontrib><title>Peak Quasisymmetric Functions and Eulerian Enumeration</title><description>Adv. Math. 176: 248--276 (2003) Via duality of Hopf algebras, there is a direct association between peak
quasisymmetric functions and enumeration of chains in Eulerian posets. We study
this association explicitly, showing that the notion of $\cd$-index, long
studied in the context of convex polytopes and Eulerian posets, arises as the
dual basis to a natural basis of peak quasisymmetric functions introduced by
Stembridge. Thus Eulerian posets having a nonnegative $\cd$-index (for example,
face lattices of convex polytopes) correspond to peak quasisymmetric functions
having a nonnegative representation in terms of this basis. We diagonalize the
operator that associates the basis of descent sets for all quasisymmetric
functions to that of peak sets for the algebra of peak functions, and study the
$g$-polynomial for Eulerian posets as an algebra homomorphism.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzr1uwjAUBWAvHSrK3qnyCyT1T3xjjwgFWgkJkNiji30jWSWmcgiCt2_TMp3hSOd8jL1KUVbWGPGO-RavpagFlLqy8MxgR_jF9yMOcbj3PV1y9Hw1Jn-J5zRwTIE344lyxMSbNPaUcWpe2FOHp4Hmj5yxw6o5LD-KzXb9uVxsCgQDhfEBNBkFlTT2918KRJKkLAakAEflOydDp-monA9CBufA10oKg8bWrtYz9vY_--duv3PsMd_byd9Ofv0DzdtADw</recordid><startdate>20070623</startdate><enddate>20070623</enddate><creator>Billera, Louis J</creator><creator>Hsiao, Samuel K</creator><creator>van Willigenburg, Stephanie</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20070623</creationdate><title>Peak Quasisymmetric Functions and Eulerian Enumeration</title><author>Billera, Louis J ; Hsiao, Samuel K ; van Willigenburg, Stephanie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a656-5cd63e526415885510aae1e28adaed6b2cf91df3eb29cd01d996c72105a587973</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Billera, Louis J</creatorcontrib><creatorcontrib>Hsiao, Samuel K</creatorcontrib><creatorcontrib>van Willigenburg, Stephanie</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Billera, Louis J</au><au>Hsiao, Samuel K</au><au>van Willigenburg, Stephanie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Peak Quasisymmetric Functions and Eulerian Enumeration</atitle><date>2007-06-23</date><risdate>2007</risdate><abstract>Adv. Math. 176: 248--276 (2003) Via duality of Hopf algebras, there is a direct association between peak
quasisymmetric functions and enumeration of chains in Eulerian posets. We study
this association explicitly, showing that the notion of $\cd$-index, long
studied in the context of convex polytopes and Eulerian posets, arises as the
dual basis to a natural basis of peak quasisymmetric functions introduced by
Stembridge. Thus Eulerian posets having a nonnegative $\cd$-index (for example,
face lattices of convex polytopes) correspond to peak quasisymmetric functions
having a nonnegative representation in terms of this basis. We diagonalize the
operator that associates the basis of descent sets for all quasisymmetric
functions to that of peak sets for the algebra of peak functions, and study the
$g$-polynomial for Eulerian posets as an algebra homomorphism.</abstract><doi>10.48550/arxiv.0706.3486</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | Peak Quasisymmetric Functions and Eulerian Enumeration |
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