correlation function can be further expressed in the form $$\begin{gathered}
\label{lt}\lim_{a\rightarrow\infty}\frac{e^{-a(d-1)}}{d} \sum_{n_{1}=0}^{\infty} \ldots \sum_{n_{d}=0}^{\infty}
\frac{a^{n_{1}+ \ldots + n_{d}}}{n_{1}! \ldots n_{d}!} \\
\nonumber \times \exp \left( \nu_{d} \sum_{D \subset [2d-2k-l]} \prod_{m \in [d]\setminus D} n_{m} 2^{|D \cap \{1,\ldots, l \}|} \right).\end{gathered}$$ The expression in the exponent can be bounded from both sides $$\begin{gathered}
\nonumber \nu_{d} 2^{l} \sum_{D \subset [2d-2k-l]} \prod_{m \in [d]\setminus D} n_{m} \leq \\
\nonumber \nu_{d} \sum_{D \subset [2d-2k-l]} \prod_{m \in [d]\setminus D}n_{m} 2^{|D \cap \{1,\ldots, l \}|} \leq \\
\nonumber \nu_{d} \sum_{D \subset [2d-2k-l]} \prod_{m \in [d]\setminus D}n_{m}.\end{gathered}$$ For the both bounding series the limit (\[lt\]) is equal to $\frac{2k-d+l}{d}$ since the series are in the form as $A(a)$ in Lemma \[lemA2\].

c\) In the previous case it can be seen the numerator is equal to number of unused orientations among facets $y_{1},\ldots,y_{2(d-k)}$ and the same applies to this calculation except that there is one extra common orientation of $x_{1}$. $\Box $

\[rmm\] In b) the limit is equal to zero for $l=d-2k.$ In this case all orientations up to the order $d$ of the submodel are exhausted. This corresponds to the situation from Theorem \[tecko\] where in (\[roj\]) also all orientations up to the order $d-k$ of 