Abstract
We present a new sieve for the distinct coordinate counting problem. This significantly improves the classical inclusion-exclusion sieve for this problem, in the sense that the number of terms is reduced from \( 2^{(_2^k )} \) to k!, and reduced further to p(k) in the symmetric case, where p(k) denotes the number of partitions of k. As an illustration of applications, we give an in-depth study of a basic example arising from coding theory and graph theory.
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Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday
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Li, J., Wan, D. A new sieve for distinct coordinate counting. Sci. China Math. 53, 2351–2362 (2010). https://doi.org/10.1007/s11425-010-3121-9
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DOI: https://doi.org/10.1007/s11425-010-3121-9