Partitions and partition numbers belong to the mathematical field of combinatorics. Partition numbers basically represent the number of ways in which we can arrange a specific set of marked or unmarked items into a sets of marked or unmarked boxes where the boxes can be either empty or not. This thesis contains presentations of all types of partition numbers but the focus is on the partition numbers where neither items nor boxes are distinguishable.
The purpose of this thesis is to present the various types of partitions and the calculation of their number in an understandable way. Partitions of unmarked items into
unmarked boxes are studied in more detail and several ways of calculating their number
are presented. The thesis also explains the correspondence between partitions and the so called Young diagrams.
An explicit closed formula for the number of partitions of unmarked items into unmarked non-empty boxes for cases where the number of boxes is less than or equal to three is obtained. A presentation of partition numbers in a matrix form is given and several interesting observations, that can be made from the corresponding matrix, are presented and proved. Some so called partition identities are presented and proved. They establish a correspondence between partitions of two different types. They are mainly proved using the notation of so called conjugate partitions.
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Ključne besede: diskretna matematika, porazdelitve, teorija števil, kombinatorika, porazdelitvena števila, porazdelitvene identitete.
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