Ein combinatorischer Satz.
Eine Ramsey-Zahl für fünf Knoten und acht Kanten.
Enumeration of concave integer partitions.
Enumeration of Lattice paths and generating functions for skew plane partitions.
Enumeration of partitions by long rises, levels, and descents.
Enumeration of symmetric arrays with different row sums
Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes.
Enumeration of unigraphical partitions.
Euler’s Partition Theorem
In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].
Examples of ε-exhaustive pathological submeasures
For any given ε > 0 we construct an ε-exhaustive normalized pathological submeasure. To this end we use potentially exhaustive submeasures and barriers of finite subsets of ℕ.
Extending a recent result of Santos on partitions into odd parts.