Accept $ { mathrm {ch}} (K) = p> 0 $ and we look at the formal power series ring $ K ((X_1, ldots, X_ {np})) $ about $ K $ in the $ np $ variables $ X_1, ldots, X_ {np} $, To let $ Lambda $ The quantity is defined as follows$ Colon $

begin {align *}

&

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}) }, \

&

{ 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 *}

Namely, $ Lambda $ is the set of departments of $ (1, ldots, np) $ in $ n $ $ “ p $-Tuple & # 39 ;.

To the $ 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 join the following ideal $ I _ { lambda} $ from $ 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 = underset { lambda in lambda} { bigcap} I _ { lambda}.

end {equation *}

Next we will specify the generators of $ S_n $ as follows$ Colon $

begin {equation *}

S_n = (θ, s_2, ldots, s_ {m (n)}),

end {equation *}

Where $ theta colon = X_1 + ldots + X_ {np} $,

## Guess. The degrees $ { mathrm {deg}} (s_2), ldots, { mathrm {deg}} (s_ {m (n)}) $ diverge if $ n to infty $,