# 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} }

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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