On the Action of Weight-Preserving Sets

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Badger, Matthew
Cwatsets; Weight-Perserving Sets; Matrix Actions; Algebra; Discrete Mathematics and Combinatorics; Mathematics
article description
We introduce weight-preserving sets of binary words. Any transformation that respects the row and column weights of a 0-1 matrix can be decomposed as a composition of two types of action on the matrix. We conjecture that weight-preserving sets perform only one type of action, permutations of rows and columns; i.e., weight-preserving sets are cwatsets.