def get_polynomial_coefficients(degree=5):
    """
    Return a list with coefficient names,
    [1  x  y  x^2  xy  y^2  x^3 ...]
    """
    names = ["1"]
    for exp in range(1, degree + 1):  # 0, ..., degree
        for x_exp in range(exp, -1, -1):
            y_exp = exp - x_exp
            if x_exp == 0:
                x_str = ""
            elif x_exp == 1:
                x_str = r"$x$"
            else:
                x_str = rf"$x^{x_exp}$"
            if y_exp == 0:
                y_str = ""
            elif y_exp == 1:
                y_str = r"$y$"
            else:
                y_str = rf"$y^{y_exp}$"
            names.append(x_str + y_str)
    return names