Eine Benutzung der Zahlenzerlegung zur Bestimmung der Anzahl unisomorpher Zyklen in -Turnieren
Entire functions on nuclear sequence spaces.
Enumeration of concave integer partitions.
Enumeration of partitions by long rises, levels, and descents.
Enumeration of symmetric arrays with different row sums
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].
Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J
We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations as single...
Extending a recent result of Santos on partitions into odd parts.