相关论文: Duality on hypermaps with symmetric or alternating…
We consider commuting pairs of holomorphic endomorphisms of P^2 with disjoint sequence of iterates. The remaining case to be studied is when their degrees coincide after some number of iterations. We show in this case that they are either…
In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…
A rectangular dual of a plane graph $G$ is a contact representations of $G$ by interior-disjoint axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. A rectangular dual…
An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
For an operator bimodule $X$ over von Neumann algebras $A\subseteq\bh$ and $B\subseteq\bk$, the space of all completely bounded $A,B$-bimodule maps from $X$ into $\bkh$, is the bimodule dual of $X$. Basic duality theory is developed with a…
A vertex $v$ in a map $M$ has the face-sequence $(p_1 ^{n_1}. \ldots. p_k^{n_k})$, if there are $n_i$ numbers of $p_i$-gons incident at $v$ in the given cyclic order, for $1 \leq i \leq k$. A map $M$ is called a semi-equivelar map if each…
We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map…
A matching in a hypergraph $\mathcal{H}$ is a set of pairwise disjoint hyperedges. The matching number $\nu(\mathcal{H})$ of $\mathcal{H}$ is the size of a maximum matching in $\mathcal{H}$. A subset $D$ of vertices of $\mathcal{H}$ is a…
We show that the mapping class group of a handlebody is a virtual duality group, in the sense of Bieri and Eckmann. In positive genus we give a description of the dualising module of any torsion-free, finite-index subgroup of the handlebody…
The classical random graph model $G(n,\lambda/n)$ satisfies a `duality principle', in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved…
Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
Let $\mathcal{H} \subseteq \binom{[n]}{r}$ be an $r$-uniform hypergraph on vertex set $[n] = \{1,2,\dots, n\}$. For an $r$-set of vertices $S \subseteq [n]$, the \emph{degree} of $S$ is defined as $\textrm{deg}(S)=\sum_{v \in…
A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
Duality is most often defined as a relationship between convex functions. If those functions are nonconvex, classical duality breaks down. Notwithstanding, we show that another kind of duality still exists, not between the functions…
We study the Aharony duality for three dimensional $\mathcal N=2$ supersymmetric gauge theories for orthogonal gauge groups with matters in vector representation. We provide the evidence for the duality by working out the partition function…
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypical example is the one of the Young graded graph of integer…
C.T.C. Wall and the first author discovered an extension of Arnold's strange duality embracing on one hand series of bimodal hypersurface singularities and on the other, isolated complete intersection singularities. In this paper, we derive…
Let $M$ be a T-motive. We introduce the notion of duality for $M$. Main results of the paper (we consider uniformizable $M$ over $F_q[T]$ of rank $r$, dimension $n$, whose nilpotent operator $N$ is 0): 1. Algebraic duality implies analytic…