Physical Sciences and Mathematics Commons^™

Packing Densities Of Colored And Non-Colored Patterns, Matthew R. Just

GS4 Georgia Southern Student Scholars Symposium

Pattern packing concerns finding an optimal permutation that contains the maximum number of occurrences of a given pattern and computing the corresponding packing density. In many instances such an optimal permutation can be characterized directly and the number of occurrences of the pattern in interest may be enumerated explicitly. In more complicated patterns a direct characterization may be more challenging, however computational results for long permutations can help provide an indirect characterization of the general form of an optimal permutation. Much work has been done on the study of pattern packing in layered patterns, as the optimal permutation of a …