Compositions with Parts Constrained by The Leading Summand

Arnold Knopfmacher1, Neville Robbins2
1THE JOHN KNOPFMACHER CENTRE FOR APPLICABLE ANALY- sis AND NUMBER THEORY, UNIVERSITY OF THE WITWATERSRAND, P. O. Wits, 2050 JOHANNESBURG, SOUTH AFRICA,
2MATHEMATICS DEPARTMENT, SAN FRANCISCO StaTE UNIVERSITY, CA 94132, U.S.A.,

Abstract

We consider compositions or ordered partitions of the natural number n for which the largest (resp. smallest) summand occurs in the first position of the composition.