Related papers: Multiple recurrence for two commuting transformati…
We establish multiple recurrence and convergence results for pairs of zero entropy measure preserving transformations that do not satisfy any commutativity assumptions. Our results cover the case where the iterates of the two…
This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving…
In arXiv:1905.08311, the author and Rohatgi proved a shuffling theorem for doubly-dented hexagons. In particular, we showed that shuffling removed unit triangles along a horizontal axis in a hexagon only changes the tiling number by a…
Starting from the cycle permutation sigma_(2^k) associated with the (2^k)-periodic orbit of the period doubling cascade we obtain the inverse permutation (sigma_(2^k))^-1. Then we build a matrix permutation related to (sigma_(2^k))^-1,…
The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different subrings of a finite non-commutative ring equals a given element of that ring. We obtain several…
In this paper, we study harmonic analysis on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. After a careful look at Frobenius reciprocity and transitivity of induction, and the…
For a highly beneficial mutant $A$ entering a randomly reproducing population of constant size, we study the situation when a second beneficial mutant $B$ arises before $A$ has fixed. If the selection coefficient of $B$ is greater than the…
Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other…
We give a new proof of Rudolph's multiple term return times theorem based on Host-Kra structure theory. Our approach provides characteristic factors for all terms, works for arbitrary tempered F{\o}lner sequences and also yields a multiple…
We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then…
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
We consider the classification, up to unitary equivalence, of commuting n-tuples of isometries. We pay special attention to the case when the product of the isometries is a shift of finite multiplicity, and we provide a complete…
Elementary MAPLE calculations are used to support the claim of hep-th/9906240 that the ratios of theta-functions, associated with the Seiberg-Witten complex curves, provide Poisson-commuting Hamiltonians which describe the dual of the…
We give here a general, best-possible, and smoothly-derived form of the Master Theorem for divide-and-conquer recurrences.
Denote by $A(p, n, k)$ the number of commuting $p$-tuples of permutations on $[n]$ that have exactly $k$ distinct orbits. It was conjectured in~\cite{abdesselam2023log} that $A(p, n, k)$ is log-concave with respect to $k$ for every $p\geq…
An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…
We investigate the possibility of Many-Body Localization in translation invariant Hamiltonian systems, which was recently brought up by several authors. A key feature of Many-Body Localized disordered systems is recovered, namely the fact…
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…