On powers of 2 dividing the values of certain plane partition functions (Q2736393)
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scientific article; zbMATH DE number 1638700
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On powers of 2 dividing the values of certain plane partition functions |
scientific article; zbMATH DE number 1638700 |
Statements
29 August 2001
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alternating sign matrices
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totally symmetric self-complementary plane partitions
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TSSCPP
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cyclially symmetric transpose complement plane partitions
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CSTCPP
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Jacobsthal numbers
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On powers of 2 dividing the values of certain plane partition functions (English)
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For a fixed prime \(p\) and a fixed positive integer \(a\), let \(\text{ord}_p(a)\) denote the highest power of \(p\) dividing \(a\). For any positive integer \(n\), let \(T(n)\) be the number of totally symmetric self-complementary plane partitions and \(C(n)\) be the number of cyclically symmetric transpose complement plane partitions in a \(2n\times 2n\times 2n\) box. The authors prove that \(\text{ord}_2(T(n))= \text{ord}_2(C(n))\).
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