Index Digest of State Constitutions

Keith, John P.; Edwards, Richard A.

doi:10.2307/3310215

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2011

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“…They used the automorphic properties to prove the existence of infinitely many congruences for k-marked Durfee symbols. Also, William J. Keith did some work on the congruential properties of k-marked Durfee symbols in [15,16]. He mainly showed that k-marked Durfee symbols of n equally populate the residue classes a and b (mod 2k + 1) if gcd(a, 2k + 1) = gcd(b, 2k + 1).…”

Section: Theorem 13 (Andrews) the Number Of Ordinary Partitions Of mentioning

confidence: 99%

The combinatorics of $k$-marked Durfee symbols

2011

Trans. Amer. Math. Soc.

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Abstract. George E. Andrews recently introduced k-marked Durfee symbols which are connected to moments of Dyson's rank. By these connections, Andrews deduced their generating functions and some combinatorial properties and left their purely combinatorial proofs as open problems. The primary goal of this article is to provide combinatorial proofs in answer to Andrews' request. We obtain a partition identity, which gives a relation between k-marked Durfee symbols and Durfee symbols by constructing bijections, and all identities on k-marked Durfee symbols given by Andrews could follow from this identity. In a similar manner, we also prove the identities due to Andrews on k-marked odd Durfee symbols combinatorially, which resemble ordinary k-marked Durfee symbols with a modified subscript and with odd numbers as entries.

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Section: Theorem 13 (Andrews) the Number Of Ordinary Partitions Of mentioning

confidence: 99%

The combinatorics of $k$-marked Durfee symbols

2011

Trans. Amer. Math. Soc.

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Index Digest of State Constitutions

Cited by 1 publication

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The combinatorics of $k$-marked Durfee symbols

The combinatorics of $k$-marked Durfee symbols

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