Geodesic
P-Partition Generating Function Equivalence of Naturally Labeled Posets
Séminaire lotharingien de combinatoire, 80B (2018) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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The P-partition generating function of a (naturally labeled) poset P is a quasisymmetric function enumerating order-preserving maps from P to Z+. Using the Hopf algebra of posets, we give necessary conditions for two posets to have the same generating function. In particular, we show that they must have the same number of antichains of each size and the same shape (as defined by Greene). We also discuss which shapes guarantee uniqueness of the P-partition generating function and give a method of constructing pairs of non-isomorphic posets with the same generating function. 

@article{SLC_2018_80B_a72,
     author = {Ricky Ini Liu and Michael Weselcouch},
     title = {P-Partition {Generating} {Function} {Equivalence} of {Naturally} {Labeled} {Posets}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a72/}
}
TY  - JOUR
AU  - Ricky Ini Liu
AU  - Michael Weselcouch
TI  - P-Partition Generating Function Equivalence of Naturally Labeled Posets
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a72/
ID  - SLC_2018_80B_a72
ER  - 
%0 Journal Article
%A Ricky Ini Liu
%A Michael Weselcouch
%T P-Partition Generating Function Equivalence of Naturally Labeled Posets
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a72/
%F SLC_2018_80B_a72
Ricky Ini Liu; Michael Weselcouch. P-Partition Generating Function Equivalence of Naturally Labeled Posets. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a72/