The asymptotics of the "strip" sums $S_\ell^{ (\al)}(n)$ and of their $d$-sums generalizations $T_{ d,ds}^{ (\al)}(dm)$ (see Definition~\ref{ definition1}) were calculated in~\cite{ regev}. It was recently noticed that when $d>1$ there is a certain confusion about the relevant notations in~\cite{ regev}, and the constant in the asymptotics of these $d$-sums $T_{ d,ds}^{ (\al)}(dm)$ seems to be off by a certain factor. Based on the techniques of~\cite{ regev} we again calculate the asymptotics of the $d$-sums $T_{ d,ds}^{ (\al)}(dm)$. We do it here carefully and with complete details. This leads to Theorem~\ref{ d.sum222} below, which replaces Corollary 4.4 of~\cite{ regev} in the cases $d>1$.
Categories: math.CO