Related papers: A Unification of Two Refinements of Euler's Partit…
Summation formulas, such as the Euler-Maclaurin expansion or Gregory's quadrature, have found many applications in mathematics, ranging from accelerating series, to evaluating fractional sums and analyzing asymptotics, among others. We show…
In this work, an expansion of Guessab-Schmeisser two points formula for n-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several…
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement…
We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function…
Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
Since the theorems of Schur and van der Waerden, numerous partition regularity results have been proved for linear equations, but progress has been scarce for non-linear ones, the hardest case being equations in three variables. We prove…
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
We give a commutative algebra viewpoint on Andrews recursive formula for the partitions appearing in "Gordon's identities", which are a generalization of Rogers-Ramanujan identities. Using this approach and differential ideals we conjecture…
We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…
We set up a combinatorial framework for inclusion-exclusion on the partitions into distinct parts to obtain an alternative generating function of partitions into distinct and non-consecutive parts. In connection with Rogers-Ramanujan…
We establish a recursive relation for the bipartition number $p_2(n)$ which might be regarded as an analogue of Euler's recursive relation for the partition number $p(n)$. Two proofs of the main result are proved in this article. The first…
Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…
We give an overpartition analogue of Bressoud's combinatorial generalization of the G\"ollnitz-Gordon theorem for even moduli in general case. Let $\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain…
Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.
We study cylindric partitions with two-element profiles using MacMahon's partition analysis. We find explicit formulas for the generating functions of the number of cylindric partitions by first finding the recurrences using partition…
Recently, Andrews and EI Bachraoui discovered several companions for some famous $q$-series formulas, and derived some new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results…
George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions. In particular, they studied the connection between two-colored partitions and overpartitions. Their proofs were analytical, but they conjectured…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…