Generalised stretched Littlewood-Richardson coefficients

In this paper we investigate Q(n) = Q λ′,μ′ (n) = P ν c(nλ + λ;nμ+ μ, ν) as a function of n and show that Q(n) is bounded above if and only if λ/μ is a partition or rotated partition. Here c(λ;μ, ν) is the LittlewoodRichardson coefficient. So Q(n) counts the number of LR tableaux of shape (nλ + λ)/(nμ + μ) or the total number of irreducible characters in the skew character [(nλ+ λ)/(nμ + μ)]. We furthermore investigate the function P (n) = P λ′,μ′,ν′ (n) = c(nλ + λ;nμ+ μ, nν + ν) as a function of n.