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We give a parametrization of the simple Bernstein components of inner forms of a general linear group over a local field by invariants constructed from type theory, and explicitly describe its behaviour under the Jacquet-Langlands…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square…
Involution words are variations of reduced words for involutions in Coxeter groups, first studied under the name of "admissible sequences" by Richardson and Springer. They are maximal chains in Richardson and Springer's weak order on…
We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding…
We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these…
In this article we focus on evolving information systems. First a delimitation of the concept of evolution is provided, resulting in a first attempt to a general theory for such evolutions. The theory makes a distinction between the…
This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it…
Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k\times k$ matrices with non-negative integer entries summing to $n$ and having no row or column of zeros. From their main theorem they…
Given a partition $\lambda$ of a number $k$, it is known that by adding a long line of length $n-k$, the dimension of the associated representation of $S_{n}$ is an integer-valued polynomial of degree $k$ in $n$. We show that its expansion…
Classical Stieltjes Transform is modified in a way to generalize both Stieltjes and Fourier transforms. This transform allows to intro- duce new classes of commutative and non-commutative generalized convolutions. Key words: Stieltjes…
We give a definition of Newton non degeneracy independent of the system of generators defining the variety. This definition extends the notion of Newton non degeneracy to varieties that are not necessarily complete intersection. As in the…
In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and…
We extend so-called slit-slide-sew bijections to constellations and quasiconstellations. We present an involution on the set of hypermaps given with an orientation, one distinguished corner, and one distinguished edge leading away from the…
Consider an involution of a smooth projective variety over a field of characteristic not two. We look at the relations between the variety and the fixed locus of the involution from the point of view of cobordism. We show in particular that…
The conventional classification schemes -- notably multinomial logistic regression -- used in conjunction with convolutional networks (convnets) are classical in statistics, designed without consideration for the usual coupling with…
Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. They were first derived in Euclidean geometry, then in Riemannian geometry. Recently they were rederived in more general case, when geometry…
A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the…
We establish a combinatorial connection between the sequence $(i_{n,k})$ counting the involutions on $n$ letters with $k$ descents and the sequence $(a_{n,k})$ enumerating the semistandard Young tableaux on $n$ cells with $k$ symbols. This…
We study the shape of the Young diagram \lambda associated via the Robinson-Schensted-Knuth algorithm to a random permutation in S_n such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other…