Related papers: Some congruences for trinomial coefficients

The classical Technical Lemma for congruences is not difficult to prove but it is very efficient in its applications. We present here a Technical Lemma for congruences on \emph{finite lattices}. This is not difficult to prove either but it…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…

We prove boundedness of rationally-connected threefolds in $\mathbb P^6$ under some extra-assumptions.

Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic…

In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients…

In this paper, we find several determinants expressing the Fibonomial coefficients. We also give the generating functions, Vandermonde identity, and continued fractions about Fibonomial coefficients.

We give a signed puzzle rule to compute Schubert coefficients. The rule is based on a careful analysis of Knutson's recurrence arXiv:math/0306304. We use the rule to prove polynomiality of the sums of Schubert coefficients with bounded…

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

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 establish a q-analogue of Wolstenholme's harmonic series congruence.

The classical modular polynomials $\Phi_\ell(X,Y)$ give plane curve models for the modular curves $X_0(\ell)/\mathbb{Q}$ and have been extensively studied. In this article, we provide closed formulas for $\ell$ nontrivial coefficients of…

We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.

We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions

This article aims to find explicit congruences between Dirichlet characters and gives various results on how to find some effectively on a computer. It ends with concrete examples putting those ideas in application.

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.

In this article we consider a method of proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we…

We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is…