login
The minimal size of a partition lambda of n such that every partition of n with at most 4 parts can be obtained by coalescing the parts of lambda.
4

%I #22 Feb 24 2020 16:40:03

%S 1,2,3,4,4,5,5,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,

%T 10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,

%U 12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14

%N The minimal size of a partition lambda of n such that every partition of n with at most 4 parts can be obtained by coalescing the parts of lambda.

%H Bo Jones and John Gunnar Carlsson, <a href="https://arxiv.org/abs/1909.09363">Minimum size generating partitions and their application to demand fulfillment optimization problems</a>, arXiv:1909.09363 [math.CO], 2019.

%F Let L(n,k) be the analogous quantity if 4 is changed to k. Then L(n,k) = 1 + L(floor(n*(k-1)/k), k) with L(0,k) = 0.

%Y Cf. A327705 (k=5), A327706 (k=6), A327707 (k=7), A327708 (k=8).

%K nonn

%O 1,2

%A _Bo Jones_, Sep 22 2019