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Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size

Guy Louchard [1]

59 109

Using the Saddle point method and multiseries expansions, we obtain from the exponential formula and Cauchy's integral formula, asymptotic results for the number $T(n,m,k)$ of partitions of $n$ labeled objects with $m$ blocks of fixed size $k$. We analyze the central and non-central region. In the region $m=n/k-n^\al,\quad 1>\al>1/2$, we analyze the dependence of $T(n,m,k)$ on $\al$. This paper fits within the framework of Analytic Combinatorics.
Set partitions, Bell numbers, Asymptotics, Saddle point method, Multiseries expansions, Analytic combinatorics
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Konular Mühendislik ve Temel Bilimler Makaleler Yazar: Guy LouchardE-posta: louchard@ulb.ac.be
 Bibtex @araştırma makalesi { jacodesmath284565, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, address = {Yıldız Teknik Üniversitesi}, year = {}, volume = {4}, pages = {75 - 91}, doi = {10.13069/jacodesmath.37019}, title = {Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size}, key = {cite}, author = {Louchard, Guy} } APA Louchard, G . (). Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size. Journal of Algebra Combinatorics Discrete Structures and Applications, 4 (1), 75-91. DOI: 10.13069/jacodesmath.37019 MLA Louchard, G . "Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (): 75-91 Chicago Louchard, G . "Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (): 75-91 RIS TY - JOUR T1 - Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size AU - Guy Louchard Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.37019 DO - 10.13069/jacodesmath.37019 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 75 EP - 91 VL - 4 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.37019 UR - http://dx.doi.org/10.13069/jacodesmath.37019 Y2 - 2018 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size %A Guy Louchard %T Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 1 %R doi: 10.13069/jacodesmath.37019 %U 10.13069/jacodesmath.37019