Related papers: Partitions versus sets : a case of duality

We point out an earlier unnoticed implication of quantum indistinguishability, namely, a property which we call `dualism' that characterizes the entanglement of two identical particles (say, two ions of the same species) -- a feature which…

A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

In his recent work, Andrews revisited two-color partitions with certain restrictions on the differences between consecutive parts, and he established three theorems linking these two-color partitions with more familiar kinds of partitions.…

A $(k,\ell )$ partial partition of an $n$-element set is a collection of $\ell $ pairwise disjoint $k$-element subsets. It is proved that, if $n$ is large enough, one can find $\left\lfloor {n\choose k}/{\ell}\right\rfloor$ such partial…

We show that the poset of non-trivial partitions of 1,2,...,n has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations…

We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…

This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…

We prove a coordinatization theorem for unital alternative algebras containing 2 x 2 matrix algebra with the same identity element 1. This solves an old problem announced by Nathan Jacobson on the description of alternative algebras…

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.

Let ${\cal E}$ be a topos, ${{\rm Dec}({\cal E}) \rightarrow {\cal E}}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg\neg} \rightarrow {\cal E}}$ be the full subcategory of double-negation sheaves. We give sufficient…

The main purpose of this article is to define the notion of DuBois singularities for pairs and proving a vanishing theorem using this new notion. The main vanishing theorem specializes to a new vanishing theorem for resolutions of log…

In this dissertation the question of the unification of quantum theory and general relativity is treated. Based on the conceptual structure of these theories and under incorporation of certain ideas from classical philosophy there are…

We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids.…

In its simplest form the Decomposition Theorem asserts that the rational intersection cohomology of a complex projective variety occurs as a summand of the cohomology of any resolution. This deep theorem has found important applications in…

We show that there is a special bijection between the indecomposable summands of the two modules which form a basic support $\tau$--tilting pair and the indecomposable summands of the two modules which form another basic support…

Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…

We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…

A generalized view of Duality is offered as a bridge between physical sciences and the more abstract philosophical dimensions bordering on mysticism. To that end several examples of duality are first cited from from conventional physics…

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…