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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-poly- nomial of a graph G is related to the Poincar´e polynomial PM(G)(z), which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a- polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multi- partite graphs G.
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참고문헌 (6)
참고문헌 신청
A. Postnikov / 2008 / Faces of generalized permutohedra / Doc. Math 13 : 207 ~ 273
A. Postnikov / 2009 / Permutohedra, associahedra, and beyond / Int. Math. Res. Not. IMRN (6) : 1026 ~ 1106
L. Comtet / 1974 / Advanced Combinatorics / D. Reidel Publishing Co
M. Aigner / 2007 / A Course in Enumeration / Springer
M. P. Carr / 2006 / Coxeter complexes and graph-associahedra / Topology Appl 153 (12) : 2155 ~ 2168
A. Postnikov / 2009 / Permutohedra, associahedra, and beyond / Int. Math. Res. Not. IMRN (6) : 1026 ~ 1106
L. Comtet / 1974 / Advanced Combinatorics / D. Reidel Publishing Co
M. Aigner / 2007 / A Course in Enumeration / Springer
M. P. Carr / 2006 / Coxeter complexes and graph-associahedra / Topology Appl 153 (12) : 2155 ~ 2168
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