AbstractK. Engel has conjectured that the average number of blocks in a partition of an n-set is a concave function of n. The average in question is a quotient of two Bell numbers less 1, and we prove Engel's conjecture for all n sufficiently large by an extension of the Moser-Wyman asymptotic formula for the Bell numbers. We also give a general theorem which specializes to an inequality about Bell numbers less complex than Engel's, in the fewer terms of the asymptotic expansion are needed to verify it for all sufficiently large n
We address the problem of closing the detection efficiency loophole in Bell experiments, which is cr...
A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a uni...
We investigate the asymptotic relation between violations of the Mermin-Belinskii-Klyshko inequality...
AbstractThe average number of distinct block sizes in a partition of a set of n elements is asymptot...
Let {bk(n)}n=0∞ be the Bell numbers of order k. It is proved that the sequence {bk(n)/n!}n=0∞ is log...
Let B. denote the number ofpartitions ofa set of n distinct objects. B. are sometimes called exponen...
AbstractThe Berry-Esséen inequality is used to obtain asymptotic solutions to a class of enumeration...
Using the Saddle point method and multiseries expansions, we obtain from the exponential formula and...
Consider n unlike objects and sets of positive integers A and B. Let S(n, A, B) be the number of par...
AbstractWe prove that the ordinary generating function of Bell numbers satisfies no algebraic differ...
Let $P(n)$ denote the number of polyominoes of $n$ cells, we show that there exist some positive num...
Heim, Neuhauser, and Tr\"oger recently established some inequalities for MacMahon's plane partition ...
The counting sequence of a special class of set partitions leads to special numbers called Bessel nu...
AbstractThe derangement problem for a ‘two-dimensional’ version of the ‘probléme des rencontres’ is ...
Let $\mathcal{A}=(a_i)_{i=1}^\infty$ be a non-decreasing sequence of positive integers and let $k\in...
We address the problem of closing the detection efficiency loophole in Bell experiments, which is cr...
A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a uni...
We investigate the asymptotic relation between violations of the Mermin-Belinskii-Klyshko inequality...
AbstractThe average number of distinct block sizes in a partition of a set of n elements is asymptot...
Let {bk(n)}n=0∞ be the Bell numbers of order k. It is proved that the sequence {bk(n)/n!}n=0∞ is log...
Let B. denote the number ofpartitions ofa set of n distinct objects. B. are sometimes called exponen...
AbstractThe Berry-Esséen inequality is used to obtain asymptotic solutions to a class of enumeration...
Using the Saddle point method and multiseries expansions, we obtain from the exponential formula and...
Consider n unlike objects and sets of positive integers A and B. Let S(n, A, B) be the number of par...
AbstractWe prove that the ordinary generating function of Bell numbers satisfies no algebraic differ...
Let $P(n)$ denote the number of polyominoes of $n$ cells, we show that there exist some positive num...
Heim, Neuhauser, and Tr\"oger recently established some inequalities for MacMahon's plane partition ...
The counting sequence of a special class of set partitions leads to special numbers called Bessel nu...
AbstractThe derangement problem for a ‘two-dimensional’ version of the ‘probléme des rencontres’ is ...
Let $\mathcal{A}=(a_i)_{i=1}^\infty$ be a non-decreasing sequence of positive integers and let $k\in...
We address the problem of closing the detection efficiency loophole in Bell experiments, which is cr...
A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a uni...
We investigate the asymptotic relation between violations of the Mermin-Belinskii-Klyshko inequality...