What Does the Future Hold for Restricted Patterns?
نویسنده
چکیده
As one can see, without several examples worked out with a pencil and paper, this formal definition is not very insightful. To understand where restricted patterns really originated from, we draw on visual imagery and replace “one-dimensional” permutations by “twodimensional” objects, matrices. In doing so, we shall violate the customary labeling of the top row as the “first” row of a matrix. Instead, we shall coordinatize our matrices from the bottom left corner, just like in a Cartesian coordinate system; thus, the origin will always be placed at the bottom left corner of the matrix (cf. Fig. 1) so that our first row will be the bottom row, and our first column will be (as usual) the leftmost column of a matrix. This is done in order to keep the resemblance with the “shape” of permutations, in other words, with their graphs as functions π : [n] → [n].
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