Symbolic method (combinatorics): Difference between revisions

Revision as of 06:48, 12 January 2015

Revision as of 06:51, 12 January 2015

Line 315:

===Boxed product===

In labelled structures, the min-boxed product <math>\mathcal{A}_{min} = \mathcal{B}^{\square}\star \mathcal{C}</math> is a variation of the origional product which requires the element of <math>\mathcal{B}</math> in the product with the minimal label. Similarly, we can also define a max-boxed product, denoted by <math>\mathcal{A}_{max} = \mathcal{B}^{\blacksquare}\star \mathcal{C}</math>, by the same manner. WeThen we have,

:<math>A_{min}(Zz)=A_{max}(Zz)=\int^{z}_{0}B'(t)C(t)dt.</math>

or equivalently,

:<math>\frac{dA_A_{min}'(Zt)}{z}=\frac{dA_A_{max}'(Zt)}{z}=\frac{dBB'(t)}{z}C(t).</math>

===Example===