Related papers: $q$-rious unimodality
We revisit Bressoud's generalized Borwein conjecture. Making use of new positivity-preserving transformations for q-binomial coefficients we establish the truth of infinitely many cases of the Bressoud conjecture. In addition, we prove new…
A combinatorial proof of the unimodality of the generalized q-Gaussian coefficients based on the explicit formula for Kostka-Foulkes polynomials is given.
Based on a classical result on partitions of an integer into a finite set of positive integers, we establish a general positivity result on coefficients of certain $q$-series which uniformly refines the positivity of truncated pentagonal…
A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
We present new proofs and generalizations of unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker…
In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank $1$, link our notion of rational singularities with the notion of rational singularities in [Kov11], and prove generalizations of standard…
Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…
In 2013, Pak and Panova proved the strict unimodality property of $q$-binomial coefficients $\binom{\ell+m}{m}_q$ (as polynomials in $q$) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients.…
In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed…
In this article, using a twisted version of H\"ormander's $L^2$-estimate, we give new characterizations of notions of partial positivity, which are uniform $q$-positivity and RC-positivity. We also discuss the definition of uniform…
We prove strict unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of S_n representations.
We answer a question posed by Michael Aissen in 1979 about the $q$-analogue of a classical theorem of George P\'olya (1922) on the algebraicity of (generalized) diagonals of bivariate rational power series. In particular, we prove that the…
We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…
A general characterization for \alpha-unimodal distributions was provided by Alamatsaz (1985) who later introduced a multivariate extension of them (Alamatsaz 1993). Here, by solving the related equations, another generalization for…
It was recently proven [Hilhorst, JSTAT, P10023 (2010)] that the q-generalization of the Fourier transform is not invertible in the full space of probability density functions for q > 1. It has also been recently shown that this…
The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…
We prove two generalisations of the Binomial theorem that are also generalisations of the q-binomial theorem. These generalisations arise from the commutation relations satisfied by the components of the co-multiplications of non-simple…
In the literature, we have several results associated with canonical decomposition of commuting contractions. In this paper, we generalize a few of these results to $Q$-commuting contractions. Here we mainly deal with $Q$-commuting and…
We establish the unimodality and the asymptotic strong unimodality of the ordinary multinomials and give their smallest mode leading to the expression of the maximal probability of convolution powers of the discrete uniform distribution. We…