Refinements of the Bell and Stirling numbers
عنوان مقاله: Refinements of the Bell and Stirling numbers
شناسه ملی مقاله: JR_COMB-7-4_004
منتشر شده در در سال 1397
شناسه ملی مقاله: JR_COMB-7-4_004
منتشر شده در در سال 1397
مشخصات نویسندگان مقاله:
Tanay Wakhare - University of Maryland
خلاصه مقاله:
Tanay Wakhare - University of Maryland
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial, restricted Bell, and $r$-derangement numbers (and probably more!). By combining methods from analytic combinatorics, umbral calculus, and probability theory, we derive several recurrence relations and closed form expressions for these numbers. By specializing our results to the classical case, we recover explicit formulae for the Bell and Stirling numbers as sums over compositions.
کلمات کلیدی: Bell numbers, Stirling numbers
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194879/