Counting faces of nestohedra
A new algebraic formula for the numbers of faces of nestohedra is obtained. The enumerator function $F(P_B)$ of positive lattice points in interiors of maximal cones of the normal fan of the nestohedron $P_B$ associated to a building set $B$ is described as a morphism from the certain combinatorial...
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| creator | Grujić, Vladimir Stojadinović, Tanja |
| description | A new algebraic formula for the numbers of faces of nestohedra is obtained.
The enumerator function $F(P_B)$ of positive lattice points in interiors of
maximal cones of the normal fan of the nestohedron $P_B$ associated to a
building set $B$ is described as a morphism from the certain combinatorial Hopf
algebra of building sets to quasisymmetric functions. We define the $q$-analog
$F_q(P_B)$ and derive its determining recurrence relations. The $f$-polynomial
of the nestohedron $P_B$ appears as the principal specialization of the
quasisymmetric function $F_q(P_B)$. |
| doi_str_mv | 10.48550/arxiv.1703.08826 |
| format | Article |
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The enumerator function $F(P_B)$ of positive lattice points in interiors of
maximal cones of the normal fan of the nestohedron $P_B$ associated to a
building set $B$ is described as a morphism from the certain combinatorial Hopf
algebra of building sets to quasisymmetric functions. We define the $q$-analog
$F_q(P_B)$ and derive its determining recurrence relations. The $f$-polynomial
of the nestohedron $P_B$ appears as the principal specialization of the
quasisymmetric function $F_q(P_B)$.</description><identifier>DOI: 10.48550/arxiv.1703.08826</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2017-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1703.08826$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1703.08826$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Grujić, Vladimir</creatorcontrib><creatorcontrib>Stojadinović, Tanja</creatorcontrib><title>Counting faces of nestohedra</title><description>A new algebraic formula for the numbers of faces of nestohedra is obtained.
The enumerator function $F(P_B)$ of positive lattice points in interiors of
maximal cones of the normal fan of the nestohedron $P_B$ associated to a
building set $B$ is described as a morphism from the certain combinatorial Hopf
algebra of building sets to quasisymmetric functions. We define the $q$-analog
$F_q(P_B)$ and derive its determining recurrence relations. The $f$-polynomial
of the nestohedron $P_B$ appears as the principal specialization of the
quasisymmetric function $F_q(P_B)$.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzs1qwkAUQOHZuBDtAwiCeYHEe-fOX5YlqC0IbrIPN5kZDWgiiRV9-6Lt6uwOnxALhEw5rWHNw6O9Z2iBMnBOmqlYFv1Pd2u7YxK5CWPSx6QL460_BT_wXEwin8fw8d-ZKLebsvhK94fdd_G5T9lYk0r2eTRQU-5NUwcIHnPtlFY1SmUpUhOIkCNYBKlyDEiOJYIm5ZVFTzOx-tu-edV1aC88PKsXs3oz6RdloDV-</recordid><startdate>20170326</startdate><enddate>20170326</enddate><creator>Grujić, Vladimir</creator><creator>Stojadinović, Tanja</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20170326</creationdate><title>Counting faces of nestohedra</title><author>Grujić, Vladimir ; Stojadinović, Tanja</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-2ad9f60b39d6cbe0ed1958454b12473f3ce331af07102491e138a210534d471d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Grujić, Vladimir</creatorcontrib><creatorcontrib>Stojadinović, Tanja</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Grujić, Vladimir</au><au>Stojadinović, Tanja</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Counting faces of nestohedra</atitle><date>2017-03-26</date><risdate>2017</risdate><abstract>A new algebraic formula for the numbers of faces of nestohedra is obtained.
The enumerator function $F(P_B)$ of positive lattice points in interiors of
maximal cones of the normal fan of the nestohedron $P_B$ associated to a
building set $B$ is described as a morphism from the certain combinatorial Hopf
algebra of building sets to quasisymmetric functions. We define the $q$-analog
$F_q(P_B)$ and derive its determining recurrence relations. The $f$-polynomial
of the nestohedron $P_B$ appears as the principal specialization of the
quasisymmetric function $F_q(P_B)$.</abstract><doi>10.48550/arxiv.1703.08826</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | Counting faces of nestohedra |
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