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Search: id:A141622
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| A141622 |
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Triangle read by rows: coefficients of chromatic polynomials for the poset of Dyck paths ordered by inclusion. |
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+0
1
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| 1, 1, 1, -1, 1, -5, 10, -9, 3, 1, -21, 210, -1321, 5823, -18968, 46908, -89034, 129490, -142270, 114532, -63791, 21940, -3499
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Number of entries in the rows are the Catalan numbers, see A000108.
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REFERENCES
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G. Berman and K. D. Fryer, Introduction to Combinatorics, Academic Press, New York, 1972.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999
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FORMULA
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C(G,t)=C(G-e,t) - C(G\e,t)
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EXAMPLE
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Chromatic polynomial for D_3 is t^5 - 5t^4 + 10t^3 - 9t^2 +3t
Table begins:
1.....................n=0
1.....................n=1
1,-1.................n=2
1,-5,10,-9,3.... n=3
...
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MAPLE
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with(networks); new(G); #this is the graph for D_3 addvertex({1, 2, 3, 4}, G); addedge(Cycle(1, 2, 3, 4), G); addvertex(5, G); addedge({4, 5}, G); draw(G); ans:=chrompoly(G, x)
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CROSSREFS
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Cf. A000108.
Sequence in context: A104645 A067843 A109360 this_sequence A144136 A144171 A001483
Adjacent sequences: A141619 A141620 A141621 this_sequence A141623 A141624 A141625
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KEYWORD
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sign,tabf
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AUTHOR
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Jennifer Woodcock (Jennifer.Woodcock(AT)ugdsb.on.ca), Aug 23 2008
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