This paper begins by extending the notion of a combinatorial configuration points and lines to planes that we refer as configurations order $2$. We then proceed investigate further extension $k$-planes ($k$-dimensional hyperplanes) which $k$. present number general examples such stacked $k$ - intuitively layering lower product discuss many analogues standard dual configurations, isomorphisms, g...

The forbidden number $\mathrm{forb}(m,F)$, which denotes the maximum of unique columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row and column permutation $F$, has been widely studied extremal set theory. Recently, this function was extended to $r$-matrices, whose entries lie $\{0,1,\dots,r-1\}$. combinatorics generalized less well-studied. In paper, we provide exact bounds fo...