Partitions, Compositions, and the Excitement of Ramanujan
Özet (Abstract): The theory of partitions concerns the representation of
integers as distinct sums of integers. For example, the
five partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1,
1 + 1 + 1 + 1.
Compositions take order into account. Thus there are 8
compositions of 4, namely 4, 3 + 1, 1 + 3, 2 + 2, 2 + 1 + 1,
1 + 2 + 1, 1 + 1 + 2, 1 + 1 + 1 + 1. Although seemingly more
complicated, compositions are much easier to study as we
Euler was the first to study partitions seriously, and
many of his discoveries are still fundamental in the subject.
In this talk we introduce the basic ideas of partitions and
compositions. We limit the necessary background to arithmetic
and a little algebra.
The talk begins with an account of compositions. The ideas
turn out to be easily understood, and the scope of the subject
is easily comprehended. We then turn to partitions, the subject
that the Indian genius Ramanujan revolutionized. We note several
themes from Ramanujan's work suggested by our study of compositions.
In each instance, we gain some appreciation of the depth and
surprise of Ramanujan's insights.
Tarih (Date): Mayıs (May) 18 Cumartesi (Saturday)
Zaman (Time): 13:00-14:00 (1:00 p.m. - 2:00 p.m.)
seminerden önce çay-kahve-kurabiye ikramı olacaktır
(tea-coffee-pastries will be served before the talk)
Yer (Loc'n): Sabancı Üniv. Karaköy İletişim Merkezi Giriş katı
(Sabancı Univ. Karaköy Communications Center Ground Floor)