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001-es BibID:	BIBFORM060340
Első szerző:	Kllogjeri, Pellumb (matematikus)
Cím:	Partition of a set with N elements into K blocks with number of elements in accordance with the composition of number N as a sum of any K natural summands (another representation of Stirling number) / Pellumb Kllogjeri, Adrian Kllogjeri
Dátum:	2013
ISSN:	2051-0845
Megjegyzések:	In the book about the generating functions (Generatingfunctionology) that is a bridge between discrete mathematics and continuous analysis, Prof. Herbert S. Wilf of University of Pennsylvania presents many of their applications. Among many other topics, treated in this book, is the one concerning the partition of a set S into blocks or parts and the respective number of partitions. The concept on the partition of a set S into k blocks is very general, meaning that each of k blocks is of any cardinality (the numbers of the elements belonging to the blocks can be different or equal).In this paper we consider the case when the number of partitions of the set [n] into k blocks and the numbers of the elements in each box are different from one another, also the combined case: the numbers of the elements in each block can be different or equal.Lastly we have presented a new formula for computing the number of partitions of the set [n] into k blocks with respect to the representation of the number n as a sum of k natural summands (different or equal). The Stirling numbers of the second kind, or Stirling partition numbers, describe the number of ways a set with n elements can be partitioned into k disjoint, non-empty subsets. Common notations are S (n, k) and, -. The study is finalized with an extraordinary identity between the second type Stirling number and the number of partitions of number n in accordance with the composition of number n with summands. We present a second way for computing the number of partitions of number n leading to the same result achieved by Stirling. The paper is a specific contribution for specific needs. It is an answer to different and specific requirements of specialists and people of different fields. Here will find answer all of those who are concerned about the number of partitions of number n into k parts with the same number of elements, with different number of elements or, several parts having the same number of elements and the others different numbers of elements.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban partition of a set partition of number n in accordance with its composition with summands classes sub-partition of rank r index of sub-partition commands
Megjelenés:	International Journal of Advanced Computing. - 46 : 3 (2013), p. 1278-1284. -
További szerzők:	Kllogjeri, Adrian
Internet cím:	Intézményi repozitóriumban (DEA) tárolt változat
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