منابع مشابه
Matricial Formulae for Partitions
X iv :0 80 6. 12 73 v1 [ m at h. N T ] 7 J un 2 00 8 MATRICIAL FORMULAE FOR PARTITIONS F. AICARDI Abstract. The exponential of the triangular matrix whose entries in the diagonal at distance n from the principal diagonal are all equal to the sum of the inverse of the divisors of n is the triangular matrix whose entries in the diagonal at distance n from the principal diagonal are all equal to t...
متن کاملConditional formulae for Gibbstype exchangeable random partitions
Gibbs–type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we investigate some properties concerning the conditional distribution of the number of blocks with a certain frequency generated by Gibbs–type random partitions...
متن کاملSome formulae for partitions into squares
We consider the problem of determining the number of partitions of a number into a fixed number of squares. This problem is distinct from, but not unrelated to, the corresponding classical problem of determining the number of representations of a number as the sum of a fixed number of squares. Whereas the classical problem has received an enormous amount of attention over the years, see Dickson...
متن کاملProduct partitions and recursion formulae
Utilizing a method briefly hinted in the author’s paper written in 1991 jointly with V. C. Harris, we derive here a number of unpublished recursion formulae for a variety of product partition functions which we believe have not been considered before in the literature. These include the functionsp∗(n;k,h) (which stands for the number of product partitions ofn> 1 into k parts of which h are dist...
متن کاملSome Summation Formulae over the Set of Partitions
Let σ(n) denote the set of partitions of n (a nonnegative integer) usually denoted by 1122 . . . nn with ∑ iki = n; ki is, of course, the number of partitions of size i. If the number of parts for the partition set of n is restricted to k, i.e., ∑ ki = k; then the corresponding subset of σ(n) is denoted by σ(n, k). For nonnegative integral vector k̄ = (k1, . . . , kn), the multinomial coefficien...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Functional Analysis and Other Mathematics
سال: 2011
ISSN: 1991-0061,1863-7914
DOI: 10.1007/s11853-011-0045-z