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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Counting hyperplane cuts vs. projections. Combinatorial identity
I believe this can be proved combinatorially. Consider we are working in the $[n_1]\times ... \times [n_d]$ box. Consider attaching a variable to each coordinate. Then consider picking an $S=i_1*x_1,. …
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Counting hyperplane cuts vs. projections. Combinatorial identity
I have checked the following combinatorial identity for several cases and it seems to work. I would like to know if this is known or if there is a counter-example. Note, i is a given constant.
$$(i+d …