TL;DR
This paper introduces the concepts of semi-canonical and canonical binary matrices, proves their correctness, and presents an algorithm using bit-wise operations to find all semi-canonical matrices with a given number of ones, relating to combinatorial matrix problems.
Contribution
It defines and mathematically validates semi-canonical and canonical binary matrices and provides an efficient algorithm for enumerating semi-canonical matrices based on their properties.
Findings
Algorithm effectively finds all semi-canonical binary matrices with specified ones.
Bit-wise operations significantly optimize the enumeration process.
The work relates to the combinatorial problem of disjoint S-permutation matrices.
Abstract
In this paper, we define the concepts of semi-canonical and canonical binary matrix. Strictly mathematical, we prove the correctness of these definitions. We describe and we implement an algorithm for finding all semi-canonical binary matrices taking into account the number of 1 in each of them. This problem relates to the combinatorial problem of finding all pairs of disjoint S-permutation matrices. In the described algorithm, the bit-wise operations are substantially used.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Advanced Mathematical Theories and Applications