Geodesic
Hook Length Property of d-Complete Posets via q-Integrals
Séminaire lotharingien de combinatoire, 80B (2018) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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The hook length formula for d-complete posets states that the P-partition generating function for them is given by a product in terms of hook lengths. We give a new proof of the hook length formula of d-complete posets using q-integrals. Proctor proved that any connected d-complete poset can be uniquely decomposed into irreducible d-complete posets and classified all irreducible d-complete posets. In this work, we prove the hook length property of all the irreducible d-complete posets. The proof is done by a case-by-case analysis consisting of two steps. First, we express the P-partition generating function for each case as a q-integral and then we evaluate the q-integrals. 

@article{SLC_2018_80B_a27,
     author = {Jang Soo Kim and Meesue Yoo},
     title = {Hook {Length} {Property} of {d-Complete} {Posets} via {q-Integrals}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a27/}
}
TY  - JOUR
AU  - Jang Soo Kim
AU  - Meesue Yoo
TI  - Hook Length Property of d-Complete Posets via q-Integrals
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a27/
ID  - SLC_2018_80B_a27
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%0 Journal Article
%A Jang Soo Kim
%A Meesue Yoo
%T Hook Length Property of d-Complete Posets via q-Integrals
%J Séminaire lotharingien de combinatoire
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%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a27/
%F SLC_2018_80B_a27
Jang Soo Kim; Meesue Yoo. Hook Length Property of d-Complete Posets via q-Integrals. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a27/