Related papers: Strictly chained (p,q)-ary partitions

We study equations of the form $\sigma(p^{q-1})=Az$, where $p$ is a prime, $q$ is a fixed odd prime, $A$ is a fixed integer and $z$ is an integer composed of primes in a fixed finite set. We shall improve upper bounds for the size and the…

We briefly review the calculational procedure for the PQCD prediction for hard exclusive quantities and reconsider the problem of the factorization scale dependence.

In this work we construct a new class of maximal partial spreads in $PG(4,q)$, that we call $q$-added maximal partial spreads. We obtain them by depriving a spread of a hyperplane of some lines and adding $q+1$ lines not of the hyperplane…

We study variants of the Erd\H os distance problem and dot products problem in the setting of the integers modulo $q$, where $q = p^{\ell}$ is a power of an odd prime.

In recent work, M. Schneider and the first author studied a curious class of integer partitions called "sequentially congruent" partitions: the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part congruent to…

Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting…

We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…

Classification of entanglement in multipartite quantum systems is an open problem solved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in…

Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their…

In a recent paper on a study of the Sylow 2-subgroups of the symmetric group with 2^n elements it has been show that the growth of the first (n-2) consecutive indices of a certain normalizer chain is linked to the sequence of partitions of…

We study the Hp-Lq boundedness of certain integral operators of fractional type.

In this note we will give various exact formulas for functions on integer partitions including the functions $p(n)$ and $p(n,k)$ of the number of partitions of $n$ and the number of such partitions into exactly $k$ parts respectively. For…

We study the boundedness of certain fractional integral operators from Hp(.) into Lq(.). We also obtain the Hp(.)- Hq(.) boundedness of the Riesz potential.

In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if $M\geq 5$ is an integer and the integers $a$ and $b$ are relatively prime to $M$ and satisfy $1\leq a<b<M/2$, and the…

For any positive integers $a$ and $b$, we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to $b$ modulo $a$. For the number of such partitions made by a…

We derive an explicit formula for a restricted partition function P_n^m(s) with constraints making use of known expression for a restricted partition function W_m(s) without constraints

The partitions of the integers can be expressed exactly in an iterative and closed-form expression. This equation is derived from distributing the partitions of a number in a network that locates each partition in a unique and orderly…

When $p$ and $q$ are coprime odd integers no less than 3, Olsson proved that the $q$-bar-core of a $p$-bar-core is again a $p$-bar-core. We establish a generalisation of this theorem: that the $p$-bar-weight of the $q$-bar-core of a bar…

We prove that the number $q(n)$ of partitions into distinct parts is log-concave for $n \geq 33$ and satisfies the higher order Tur\'an inequalities for $n\geq 121$ conjectured by Craig and Pun. In doing so, we establish explicit error…

We calculate fragmentation functions for a b-quark to fragment into color-singlet P-wave bound states $\bar c b$ in the Heavy Quark Effective Theory with the exact account of $O(1/m_b)$ corrections. We demonstrate an agreement of the…