Related papers: Symmetric multisets of permutations
We involve simultaneously the theory of matched pairs of groups and the theory of braces to study set-theoretic solutions of the Yang-Baxter equation (YBE). We show the intimate relation between the notions of a symmetric group (a braided…
Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. In this paper, the Conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and St\u{a}nic\u{a}…
This paper is the first in a series which aims at: (a) giving a proof that the associator relations between multizeta values imply the double shuffle and regularization (DSR) ones, alternative to that of the second-named author's 2010…
We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The `quantization commutes with reduction' conjecture of Guillemin and…
We construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence…
We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We…
The systematic study of inversion sequences avoiding triples of relations was initiated by Martinez and Savage. For a triple $(\rho_1,\rho_2,\rho_3)\in\{<,>,\leq,\geq,=,\neq,-\}^3$, they introduced $\I_n(\rho_1,\rho_2,\rho_3)$ as the set of…
For a class of symplectic manifolds, we introduce a functional which assigns a real number to any pair of continuous functions on the manifold. This functional has a number of interesting properties. On the one hand, it is Lipschitz with…
Motivated by a question in Schubert calculus, we study the interplay of quasisymmetric polynomials with the divided symmetrization operator, which was introduced by Postnikov in the context of volume polynomials of permutahedra. Divided…
Let $K$ be a field and let $\mathbb N = \{1,2, \dots \}$. Let $R_n=K[x_{ij} \mid 1\le i\le n, j\in \mathbb N]$ be the ring of polynomials in $x_{ij}$ $(1 \le i \le n, j \in \mathbb N)$ over $K$. Let $S_n = Sym (\{1,2, \ldots, n \})$ and…
(Abridged abstract) For a finite real reflection group W and a W-orbit O of flats in its reflection arrangement---or equivalently a conjugacy class of its parabolic subgroups---we introduce a statistic on elements of W. We then study the…
The nonzero level sets in $n$-dimensional flat affine space of a translationally homogeneous function are improper affine spheres if and only if the Hessian determinant of the function is equal to a nonzero constant multiple of the $n$th…
The class of quasisymmetric mappings on the real axis was first introduced by A. Beurling and L. V. Ahlfors in 1956. In 1980 P. Tukia and J. V\"{a}is\"{a}l\"{a} considered these mappings between general metric spaces. In our paper we…
We prove a conjecture of J.-C. Novelli, J.-Y. Thibon, and L. K. Williams (2010) about an equivalence of two triples of statistics on permutations. To prove this conjecture, we construct a bijection through different combinatorial objects,…
We define a new basis of quasisymmetric functions, the row-strict dual immaculate functions, as the generating function of a particular set of tableaux. We establish that this definition gives a function that can also be obtained by…
In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets,…
Mason and Remmel introduced a basis for quasisymmetric functions known as the row-strict quasisymmetric Schur functions. This basis is generated combinatorially by fillings of composition diagrams that are analogous to the row-strict…
Dyson's (1962) classification of matrix ensembles is reviewed from a modern perspective, and its recent extension to disordered fermion problems is motivated and described. It is explained in particular why symmetry classes are associated…
It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.
According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of indistinguishable objects?". This is the aim of quasi-set…