Processes of rth largest

Random Partitions with Non Negative rth Differences

Let Pr(n) be the set of partitions of n with non negative r th differences. Let λ be a partition of an integer n chosen uniformly at random among the set Pr(n) Let d(λ) be a positive r th difference chosen uniformly at random in λ. The aim of this work is to show that for every m ≥ 1, the probability that d(λ) ≥ m approaches the constant m−1/r as n → ∞ This work is a generalization of a result ...

Another story of mice and men: the types of RTH.

T he syndrome of resistance to thyroid hormone (RTH) is an inherited autosomal dominant human disease (1). It is most commonly caused by point mutations in the THRB gene that encodes TR , 1 of 2 thyroid hormone (TH) receptors (TRs) in humans (2, 3). TRs are ligand-gated transcription factors (4), and most RTH mutations affect the C-terminal ligand-binding domain and reduce TR affinity for hormo...

The rth Moment of the Divisor Function: An Elementary Approach

On the absolute Nqα -summability of rth derived conjugate series

In the year 1921, Nevanlinna [7] suggested and discussed an interesting method of summation called Nq-method. Moursund [5] applied this method for summation of Fourier series and its conjugate series. Later, Moursund [6] developed Nqp-method (where p is a positive integer) and applied it to pth derived Fourier series. Samal [9] discussed Nqαmethod (0 ≤ α < 1) and studied absolute Nqα-summabilit...

The Rth Smallest Part Size of a Random Integer Partition

We study the size of the rth smallest part and the rth smallest distinct part in a random integer partition. This extends the research on partitions with no small parts of Nicolas and Sárközy. – To the memory of Nicolaas Govert (Dick) de Bruijn