Related papers: The peak statistics on simsun permutations
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
In the present article we introduce three new notions which are called Gaussian Mersenne Lucas numbers, Mersenne Lucas polynomials and Gaussian Mersenne Lucas polynomials. We present and prove our exciting properties and results of them…
For a prime p>2 and q=p^n, we compute a finite generating set for the SL_2(F_q)-invariants of the second symmetric power representation, showing the invariants are a hypersurface and the field of fractions is a purely transcendental…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological…
We describe some configurations of conjugate permutations which may be used as a mathematical model of some genetical processes and crystal growth.
In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational R\'{e}dei functions. A complete characterization of their compositional inverses is also given. These…
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also…
We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
In this study, we apply the binomial transforms to Tribonacci and Tribonacci-Lucas sequences. Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we illustrate the…
The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair…
In this paper we collect some results about arithmetic progressions of higher order, also called polynomial sequences. Those results are applied to $(m,q)$-isometric maps.
Let $S_n$ denote the group all permutations of $n$. For every permutation $\sigma$, we let $\mathrm{des}(\sigma)$ denote the number of descents in $\sigma$ and $\mathrm{LRMin}(\sigma)$ denote the number of left-to-right minima of $\sigma$.…
A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…
In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating…
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in…