assume $ { mathrm {ch}} (K) = p> 0 $ and we consider the ring of the formal power series $ K ((X_1, ldots, X_ {np})) $ more than K $ in $ np $ the variables $ X_1, ldots, X_ {np} $. Let $ Lambda $ be set as follows$ colon $

begin {align *}

And

Lambda colon ! = { Mathrm {all ~ sets ~}} {(i_1, ldots, i_p), (i_ {p + 1}, ldots, i_ {2p}), ldots, (i_ {(n-1) p + 1}, ldots, i_ {np}) }, \

And

{ mathrm {where}}, ~ {1, 2, 3, 4, ldots } = {i_1, i_2, i_3, i_4, ldots } phantom {I} { mathrm {st}} phantom {I} i_k not = i_l phantom {I} { mathrm {for}} phantom {i} k not = l.

end {align *}

To know, $ Lambda $ is the whole of the divisions of $ (1, ldots, np) $ in $ n $ $ “ p $-tuples & # 39;

For $ lambda = {(i_1, ldots, i_p), (i_ {p + 1}, ldots, i_ {2p}), ldots, (i _ {(n-1) p + 1}, ldots, i_ {np}) } in Lambda $we will associate the following ideal $ I _ { lambda} $ of $ A _ { infty} $$ colon $

begin {equation *}

I _ { lambda} colon ! = (X_ {i_1} + ldots + X_ {i_p}, X_ {i_ {p + 1}} + ldots + X_ {i_ {2p}}, ldots, X_ {(n-1) p + 1} + ldots + X_ {np}).

end {equation *}

We will define the ideal $ S_n $ of the ring $ K ((X_1, ldots, X_ {np})) $ by the following$ colon $

begin {equation *}

S_n colon = subset { lambda in Lambda} { bigcap} I _ { lambda}.

end {equation *}

In addition, we will specify the generators of $ S_n $ as following$ colon $

begin {equation *}

S_n = ( theta, s_2, ldots, s_ {m (n)}),

end {equation *}

or $ theta colon = X_1 + ldots + X_ {np} $.

## Conjecture. Degrees $ { mathrm {deg}} (s_2), ldots, { mathrm {deg}} (s_ {m (n)}) $ diverge when $ n to infty $.