论文标题
对称组的周期指标的一致性
Congruences for the cycle indicator of the symmetric group
论文作者
论文摘要
令$ n $为正整数，让$ c_n $为对称组$ s_n $的周期指标。 Carlitz证明，如果$ p $是素数，并且如果$ r $是一个非负整数，那么我们有一致性$ c_ {r+np} \ equiv（x_1^p-x_p）^nc_r \ mod {pz_p [x_1，\ cdots，x_ {r+np}]}，其中$ z_p $是$ p $ -Adic Integers的戒指。我们证明，对于$ p \ neq 2 $，前面的一致性保留modulo $ npz_p [x_1，\ cdots，x_ {r+np}] $。这使我们可以证明Meixner多项式的Junod猜想。
Let $n$ be a positive integer and let $C_n$ be the cycle indicator of the symmetric group $S_n$. Carlitz proved that if $p$ is a prime, and if $r$ is a non negative integer, then we have the congruence $C_{r+np}\equiv (X_1^p-X_p)^nC_r \mod{pZ_p[X_1,\cdots,X_{r+np}]},$ where $Z_p$ is the ring of $p$-adic integers. We prove that for $p\neq 2$, the preceding congruence holds modulo $npZ_p[X_1,\cdots,X_{r+np}]$. This allows us to prove a Junod's conjecture for Meixner polynomials.
