The Andrews–Gordon Identities and q-Multinomial Coefficients

@article{Warnaar1997TheAI,
  title={The Andrews–Gordon Identities and q-Multinomial Coefficients
},
  author={S. Ole Warnaar},
  journal={Communications in Mathematical Physics},
  year={1997},
  volume={184},
  pages={203-232}
}
  • S. Warnaar
  • Published 15 January 1996
  • Mathematics, Physics
  • Communications in Mathematical Physics
Abstract: We prove polynomial boson-fermion identities for the generating function of the number of partitions of n of the form $n=\sum_{j=1}^{L-1} j f_j$, with $f_1\leq i-1$, $f_{L-1} \leq i'-1$ and $f_j+f_{j+1}\leq k$. The bosonic side of the identities involves q-deformations of the coefficients of xa in the expansion of $(1+x+\cdots+ x^k)^L$. A combinatorial interpretation for these q-multinomial coefficients is given using Durfee dissection partitions. The fermionic side of the… 

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