How do i express a chromatic polynomial as a falling factorial function?
[attachment=0:szbeqan8]Capture.JPG[/attachment:szbeqan8]
I understand the joinproduct, but it seems that in order to apply it I'd need to convert the chromatic polynomials into falling factorial functions :?
like \(\displaystyle p(P_{3},x) = x(x1)^{2}\)
and \(\displaystyle p(C_{4},x) = (x1)^{4} + (x1)\)
and i dunno how to express that as a falling factorial :
edit: i think i kinda get it .... but i'm getting:
\(\displaystyle p(P_{3},x) = x^32x^2+x = x^{(3)}+x^{(2)}\)
\(\displaystyle p(C_{4},x) = x^44x^3+6x^23x = x^{(4)}+2x^{(3)}+x^{(2)}\)
and \(\displaystyle (x^{(3)}+x^{(2)})\vee(x^{(4)}+2x^{(3)}+x^{(2)})\not=x(x1)(x2)(x3)(x^3 12x^2 + 50x71)\) :cry:
edit2: holy crap, it totally does = :shock:
thanks everybody XD this is why i love this forum ... even when noone's responding it's still helpful XD
my only question left is how do i do this without actually drawing out all the picture and using chromatic reduction? :shock:
[attachment=0:szbeqan8]Capture.JPG[/attachment:szbeqan8]
I understand the joinproduct, but it seems that in order to apply it I'd need to convert the chromatic polynomials into falling factorial functions :?
like \(\displaystyle p(P_{3},x) = x(x1)^{2}\)
and \(\displaystyle p(C_{4},x) = (x1)^{4} + (x1)\)
and i dunno how to express that as a falling factorial :
edit: i think i kinda get it .... but i'm getting:
\(\displaystyle p(P_{3},x) = x^32x^2+x = x^{(3)}+x^{(2)}\)
\(\displaystyle p(C_{4},x) = x^44x^3+6x^23x = x^{(4)}+2x^{(3)}+x^{(2)}\)
and \(\displaystyle (x^{(3)}+x^{(2)})\vee(x^{(4)}+2x^{(3)}+x^{(2)})\not=x(x1)(x2)(x3)(x^3 12x^2 + 50x71)\) :cry:
edit2: holy crap, it totally does = :shock:
thanks everybody XD this is why i love this forum ... even when noone's responding it's still helpful XD
my only question left is how do i do this without actually drawing out all the picture and using chromatic reduction? :shock:
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