TY - JOUR

T1 - A simple and direct derivation for the number of noncrossing partitions

AU - Liaw, S. C.

AU - Yeh, H. G.

AU - Hwang, F. K.

AU - Chang, G. J.

PY - 1998

Y1 - 1998

N2 - Kreweras considered the problem of counting noncrossing partitions of the set {1,2, ..., n}, whose elements are arranged into a cycle in its natural order, into p parts of given sizes n1,n2, ... ,np (but not specifying which part gets which size). He gave a beautiful and surprising result whose proof resorts to a recurrence relation. In this paper we give a direct, entirely bijective, proof starting from the same initial idea as Kreweras' proof.

AB - Kreweras considered the problem of counting noncrossing partitions of the set {1,2, ..., n}, whose elements are arranged into a cycle in its natural order, into p parts of given sizes n1,n2, ... ,np (but not specifying which part gets which size). He gave a beautiful and surprising result whose proof resorts to a recurrence relation. In this paper we give a direct, entirely bijective, proof starting from the same initial idea as Kreweras' proof.

UR - http://www.scopus.com/inward/record.url?scp=22044446927&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-98-04546-8

DO - 10.1090/s0002-9939-98-04546-8

M3 - 期刊論文

AN - SCOPUS:22044446927

VL - 126

SP - 1579

EP - 1581

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -