- Volume 52 Issue 2
DOI QR Code
SIGNED A-POLYNOMIALS OF GRAPHS AND POINCARÉ POLYNOMIALS OF REAL TORIC MANIFOLDS
- Seo, Seunghyun (Department of Mathematics Education Kangwon National University) ;
- Shin, Heesung (Department of Mathematics Inha University)
- Received : 2013.11.24
- Published : 2015.03.31
Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the
- M. Aigner, A Course in Enumeration, Graduate Texts in Mathematics, vol. 238, Springer, Berlin, 2007.
- M. P. Carr and S. L. Devadoss, Coxeter complexes and graph-associahedra, Topology Appl. 153 (2006), no. 12, 2155-2168. https://doi.org/10.1016/j.topol.2005.08.010
- S. Choi and H. Park, A new graph invariant arises in toric topology, accepted in J. Math. Soc. Japan (2014), available at arXiv:1210.3776.
- L. Comtet, Advanced Combinatorics, enlarged ed., D. Reidel Publishing Co., Dordrecht, 1974
- A. Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. IMRN (2009), no. 6, 1026-1106.
- A. Postnikov, V. Reiner, and L. Williams, Faces of generalized permutohedra, Doc. Math. 13 (2008), 207-273.