Related papers: The uniqueness of plethystic factorisation

We prove several unique prime factorization results for tensor products of type II_1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1.…

The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi…

We give a short proof -- not relying on ideal classes or the geometry of numbers -- of a known criterion for quadratic orders to possess unique factorization.

We prove that every holomorphic symplectic matrix can be factorized as a product of holomorphic unitriangular matrices with respect to the symplectic form $ \left[\begin{array}{ccc} 0 & L_n \\ -L_n & 0\end{array}\right]$ where $L$ is the $n…

We prove that all Mathieu groups, some linear, and unitary groups are factorizable.

We prove that a functional with Lipschitzian derivative, when restricted to suitable spheres centered at a noncritical point, has a unique maximum.

Gurevich, Pyatov and Saponov recently stated an expansion for the product of two Schur functions and gave a proof based on the Pluecker relations. Here we show that this identity is in fact a special case of a quite general Schur function…

We analyse partitions of products with two ordered factors in two classes where both factors are countable or well-ordered and at least one of them is countable. This relates the partition properties of these products to cardinal…

We proved the factorization of generalized theta functions when the curve has two irreducible components meeting at one node.

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.

Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.

This paper classifies the factorizations of almost simple groups with a factor having at least two nonsolvable composition factors. This together with a previous classification result of the authors reduces the factorization problem of…

We give a formula for the number of irreducibles (with multiplicity) in the decomposition of the plethysm $s_\lambda[s_m]$ of Schur functions in terms of the number of lattice points in certain rational polytopes. In the case where $\lambda…

We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…

Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

Shimura proved that each principally polarized abelian variety over $\mathbf{C}$ admits a unique factorization into irreducible principally polarized abelian varieties. We give an exposition of his result, and generalize to an arbitrary…

We consider a derivation $\mathsf{D}$ on the ring $\Lambda$ of symmetric functions and investigate its combinatorial, algebraic and geometric properties. More precisely, we show that $\mathsf{D}$ restricts to a quasi-isometry, with respect…

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…

Elementary proofs are given for sums of Schur functions over partitions into at most n parts each less than or equal to m for which i) all parts are even, ii) all parts of the conjugate partition are even. Also, an elementary proof of a…