منابع مشابه
Multiplicative Partitions
New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.
متن کاملArithmagons and Geometrically Invariant Multiplicative Integer Partitions
In this article, we introduce a formal definition for integral arithmagons. Informally, an integral arithmagon is a polygonal figure with integer labeled vertices and edges in which, under a binary operation, adjacent vertices equal the included edge. By considering the group of automorphisms for the associated graph, we count the number of integral arithmagons whose exterior sum or product equ...
متن کاملA “Fourier Transform” for Multiplicative Functions on Non-Crossing Partitions
We describe the structure of the group of normalized multiplicative functions on lattices of noncrossing partitions. As an application, we give a combinatorial proof of a theorem of D. Voiculescu concerning the multiplication of free random variables.
متن کاملNormal Convergence for Random Partitions with Multiplicative Measures
Let Pn be the space of partitions of integer n ≥ 0, P the space of all partitions, and define a class of multiplicative measures induced by Fβ(z) = ∏ k(1 − zk)k β with β > −1. Based on limit shapes and other asymptotic properties studied by Vershik, we establish normal convergence for the size and parts of random partitions.
متن کاملMULTIPLICATIVE PROPERTIES OF THE NUMBER OF k-REGULAR PARTITIONS
In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with k-regular partitions. Extending the generating function for k-regular partitions multiplicatively to a function on k-regular partitions, we show that it takes its maximum at an explicitly described small set of partitions, and can thus easily be...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2977