Related papers: Supercongruences for sporadic sequences
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…
The present study provides another look on Lamperti's theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti's theorem and the recent result by the author [V. M. Abramov, Theor. Probab. Math.…
In this paper we study some basic properties of rough $I$-convergent double sequences in the line of D$\ddot{u}$ndar [8]. We also study the set of all rough $I$-limits of a double sequence and relation between boundedness and rough…
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…
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…
Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite…
We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.
The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…
We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime and m, s, r are positive integers. These…
We generalize recent developments on normal forms and the spectral sequences method to make a foundation for parametric normal forms. We further introduce a new style and costyle to obtain unique parametric normal forms. The results are…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
Recently, generalizations of the classical Three Gap Theorem to higher dimensions attracted a lot of attention. In particular, upper bounds for the number of nearest neighbor distances have been established for the Euclidean and the maximum…
We prove coherence theorems for bicategories, pseudofunctors and pseudonatural transformations. These theorems boil down to proving the coherence of some free $(4,2)$-categories. In the case of bicategories and pseudofunctors, existing…
We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…
In this paper we give an overview of recent results on (upper and lower) discrepancy estimates for (concrete) sequences in the unit-cube. In particular we also give an overview of discrepancy estimates for certain classes of hybrid…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
In this paper we get two new classes of regular sequences in the polynomial ring over the field of complex numbers.
This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…