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Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture
1. The conjecture 2. Fundamental structures 3. Lattice paths and plane partitions 4. Symmetric functions 5. Hypergeometric series 6. Explorations 7. Square ice.
  • 443
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Some identities for terminating q-series
We present the following sequence of polynomial identities: is the Gaussian polynomial denned to be zero for m m > N , one for m = 0 or N and
  • 80
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A Generalization of the Rogers-Ramanujan Identities for all Moduli
  • D. Bressoud
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 July 1979
TLDR
We extend the Rogers-Ramanujan identities to all even moduli, and provide a theorem which holds for all moduli. Expand
  • 68
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A proof of Andrews' q-Dyson conjecture
TLDR
We prove that the constant term of the Laurent polynomial @?"1" =<"i"<"j"=<"n(x"i/x"j)"a"""i(qx" j/ x"i)" a"""j, where x"1,...,x"n,q are commuting indeterminates and a" 1,...,a"n are non-negative integers. Expand
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  • 11
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Lattice Path and the Rogers-Ramanujan Identities
This is an exposition and elaboration on work of W.H. Burge which demonstrates the connections among the various combinatorial interpretations of the multiple summations which arise inExpand
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  • 11
Factorization and Primality Testing
TLDR
This is a discussion of number theory, covering factorization and primality testing. Expand
  • 125
  • 9
Undergraduate Programs and Courses in the Mathematical Sciences: Cupm Curriculum Guide 2004
TLDR
Algebra: Modular arithmetic, permutations, group theory through isomorphism theorems, ring theory through the notions of prime and maximal ideals; additional topics such as unique factorization domains and classification of groups of small order. Expand
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