No requirement for equal-sized subsets is mentioned.";
                case 1:
                    return "Here \\(\\boldsymbol{\\mu}_i \\in \\mathbb{R}^d\\) is the representative -- or center -- of cluster \\(C_i\\).";
                case 2:
                    return "The \\(k\\)-means objective is defined in the text as minimizing the sum of squared distances between data points and their assigned cluster centers.";
                case 3:
                    return "An optimal partition under the objec