Symbolic method (combinatorics): Difference between revisions

Revision as of 05:58, 12 January 2015

Revision as of 06:41, 12 January 2015

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:<math>A(z) = \sum_{k = 0}^{\infty} \frac{B(z)^k}{k} = \ln\left(\frac{1}{1-B(z)}\right).</math>

===Boxed produuctproduct===

In labelled structures, the min-boxed product <math>\mathcal{A}_{min} = \mathcal{B}^{\square}\star \mathcal{C}</math> is dfineddefined as the product construction with one more requirement that the element with smallest label is in <math>\mathcal{B}</math>. Similar, we can defined a max-boxed product and denoted by <math>\mathcal{A}_{max} = \mathcal{B}^{\blacksquare}\star \mathcal{C}</math>, where the element with largest label is in <math>\mathcal{B}</math>. We have,

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

or says,