@article{oai:muroran-it.repo.nii.ac.jp:00010028,
 author = {TAKEGAHARA,  Yugen and 竹ケ原, 裕元},
 journal = {Advances in Mathematics},
 month = {Jun},
 note = {application/pdf, Let p be a prime, and let G be a finite abelian p-group of type λ=(λ1,λ2,…) with λ1≥λ2≥⋯ and ∑λi=s. Set u=max⁡{λ1,[(s+1)/2]} and v=s−u. For each nonnegative integern, let hn(G) be the number of homomorphisms from G to the symmetric group Sn on n letters. Except for the case where p=2and u+δv0≤v+1, δ the Kronecker delta, or p=3 and u=v≥1, there exist p-adic analytic functions fr(X) for r=0,1,…,pu+1−1and a polynomial η(X) with integer coefficients such that for any nonnegative integer y, hpu+1y+r(G)=p{∑j=1upj−(u−v)}yfr(y)∏j=1yη(j)and ordp(hpu+1y+r(G))={∑j=1upj−(u−v)}y+ordp(fr(y)). If p=2, λ3=0, and u=v≥1 or if p=3 and u=v≥1, then hn(G) has analogous properties. Under the assumption that λ3=0, some results for the number of permutation representations of G in the wreath product of a cyclic group of order p with Sn are also presented.},
 pages = {367--425},
 title = {p-adic Estimates of the Number of Permutation Representations},
 volume = {349},
 year = {2019},
 yomi = {タケガハラ, ユウゲン}
}