相关论文: Composing (with) automorphisms in the colored Cube…

A binary linear code whose permutation automorphism group has a fixed point free permutation of order $3$ is called a binary cubic code. The scope of this paper is to investigate the structural properties of binary cubic codes. Let $C$ be a…

We study the graph isomorphism game that arises in quantum information theory from the perspective of bigalois extensions of compact quantum groups. We show that every algebraic quantum isomorphism between a pair of (quantum) graphs $X$ and…

We study the arithmetic codings of hyperbolic automorphisms of the 2-torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet endowed with an appropriate structure of additive group onto…

The Glauber dynamics on the colourings of a graph is a random process which consists in recolouring at each step a random vertex of a graph with a new colour chosen uniformly at random among the colours not already present in its…

We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…

In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…

Babel has shown that for an extended class of chordal (6, 3) graphs the coarsest regular simplicial partition is equivalent to the graph's automorphism partition. We give a reversible transformation for any graph to one of these graph by…

We study the chromatic quasisymmetric class function of a linearized combinatorial Hopf monoid. Given a linearized combinatorial Hopf monoid $H$, and an $H$-structure $h$ on a set $N$, there are proper colorings of $h$, generalizing graph…

In this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad.…

A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These…

Dance and music are two highly correlated artistic forms. Synthesizing dance motions has attracted much attention recently. Most previous works conduct music-to-dance synthesis via directly music to human skeleton keypoints mapping.…

Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…

We introduce a novel combinatorial method to study $Q^{**}$-transformations of group presentations or, equivalently, 3-deformations of CW-complexes of dimension 2. Our procedure is based on a refinement of discrete Morse theory that gives a…

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…

We study smooth cubic fourfolds admitting an automorphism of order $7$. It is known that the possible symplectic automorphism groups of such cubic fourfolds are precisely $F_{21}$, $\mathrm{PSL}(2,\mathbb{F}_7)$, and $A_7$. In this paper,…

We present a combinatorial isomorphism between Stasheff associahedra and an inductive cone construction of those complexes given by Loday. We give an alternate description of certain polytopes, known as multiplihedra, which arise in the…

We prove that $Aut({\mathbb S}^1)$ coincides with the automorphism group of the \emph{circle graph} $\mathcal{C}$, i.e. the intersection graph of the family of chords of ${\mathbb S}^1$. We prove that the countable subgraph of $\mathcal{C}$…

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently…

We present Music102, an advanced model aimed at enhancing chord progression accompaniment through a $D_{12}$-equivariant transformer. Inspired by group theory and symbolic music structures, Music102 leverages musical symmetry--such as…

Melody harmonization has long been closely associated with chorales composed by Johann Sebastian Bach. Previous works rarely emphasised chorale generation conditioned on chord progressions, and there has been a lack of focus on assistive…