  We consider partition functions on the $N\times N$ square lattice with the
local Boltzmann weights given by the $R$-matrix of the
$U_{t}(\widehat{sl}(n+1|m))$ quantum algebra. We identify boundary states such
that the square lattice can be viewed on a conic surface. The partition
function $Z_N$ on this lattice computes the weighted sum over all possible
closed coloured lattice paths with $n+m$ different colours: $n$ ``bosonic''
colours and $m$ ``fermionic'' colours. Each bosonic (fermionic) path of colour
$i$ contributes a factor of $z_i$ ($w_i$) to the weight of the configuration.
We show the following. (i) $Z_N$ is a symmetric function in the spectral
parameters $x_1\dots x_N$ and generates basis elements of the commutative
trigonometric Feigin--Odesskii shuffle algebra. The generating function of
$Z_N$ admits a shuffle-exponential formula analogous to the Macdonald Cauchy
kernel. (ii) $Z_N$ is a symmetric function in two alphabets $(z_1\dots z_n)$
and $(w_1\dots w_m)$. When $x_1\dots x_N$ are set to be equal to the box
content of a skew Young diagram $\mu/\nu$ with $N$ boxes the partition function
$Z_N$ reproduces the skew Macdonald function $P_{\mu/\nu}\left[w-z\right]$.
