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Recently, a class of partition functions associated with higher rank rationaland trigonometric integrable models were introduced by Foda and Manabe. We usethe dynamical $R$-matrix of the elliptic quantum group $E_{\tau,\eta}(gl_3)$ tointroduce an elliptic analogue of the partition functions associated with$E_{\tau,\eta}(gl_3)$. We investigate the partition functions of Foda-Manabetype by developing a nested version of the elliptic Izergin-Korepin analysis,and present the explicit forms as symmetrization of multivariable ellipticfunctions. We show that special cases are essentially the elliptic weightsfunctions introduced in the works by Rim\'anyi-Tarasov-Varchenko, Konno,Felder-Rim\'anyi-Varchenko.

A class of partition functions associated with $E_{\tau,\eta}(gl_3)$ by Izergin-Korepin analysis