Related papers: Some symmetric $q$-congruences
We give a sufficient condition for isometric actions to have the congruency of orbits, that is, all orbits are isometrically congruent to each other. As applications, we give simple and unified proofs for some known congruence results, and…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
We classify the $Q$-homogeneous skew Schur $Q$-functions, i.e., those of the form $Q_{\lambda/\mu} = k \cdot Q_{\nu}$. On the way we develop new tools that are useful also in the context of other classification problems for skew Schur…
In this paper, we prove certain theorems about three consecutive primes.
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
Classical Sturm-Liouville problems of $q$-difference variables are extended for symmetric discrete functions such that the corresponding solutions preserve the orthogonality property. Some illustrative examples are given in this sense.
In this paper, we establish some Fleck-Weisman type and Davis-Sun type congruences for the Stirling numbers and the Eulerian numbers.
We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove $k$-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound…
We give some new $q$-supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The…
We prove the splitting of the Kummer exact sequence and related exact sequences in arithmetic geometry.
We prove some integral inequalities related to Feng Qi's inequality (2000) and obtain a few corollaries.
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary…
Guillera and Zudilin proved three "divergent" Ramanujan-type supercongruences by means of the Wilf-Zeilberger algorithmic technique. In this paper, we prove $q$-analogues of two of them via the $q$-WZ method. Additionally, we give…
We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral…
We use an elementary argument to prove some finite sums involving expressions of the forms $(q)_n$ and $(a;q)_n$ along with inductive formulas for some sequences.
An $n\times n$ real matrix $Q$ is quasi-orthogonal if $Q^{\top}Q=qI_{n}$ for some positive real number $q$. If $M$ is a principal sub-matrix of a quasi-orthogonal matrix $Q$, we say that $Q$ is a quasi-orthogonal extension of $M$. In a…
Recently, the higher-order q-Euler polynomials and multiple q-Euler zeta functions are introduced by T. Kim ([8, 9]). In this paper, we investigate some symmetric properties of the multiple q-Euler zeta function and derive various…