Related papers: On Zeilberger Conjecture
This partly expository paper investigates versions of the Tate conjecture on the cycle map for varieties defined over finite fields with values in 'etale cohomology with Z_\ell-coefficients. The bulk of the paper is an exposition of a 1998…
We prove a conjecture of Johann Cigler on shifted Hankel determinants.
We prove a conjecture of Meszaros and Morales on the volume of a flow polytope. Independently from our work, Zeilberger sketched a proof of their conjecture. In fact, our proof is the same as Zeilberger's proof. The purpose of this note is…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
In this short note, we revisit Zeilberger's proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.
We use the homological perturbation lemma to give an explicit proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.
Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a…
Stickelberger proved that the discriminant of a number field is congruent to 0 or 1 modulo 4. We generalize this to an arbitrary (not necessarily commutative) ring of finite rank over the integers using techniques from linear algebra. Our…
In this paper, we prove a conjecture of Schnell in the surface case.
We prove a conjectured relationship among resultants and the determinants arising in the formulation of the method of moving surfaces for computing the implicit equation of rational surfaces formulated by Sederberg. In addition, we extend…
Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p-adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant,…
In his book Topics in Analytic Number Theory, Rademacher considered the generating function of partitions into at most $N$ parts, and conjectured certain limits for the coefficients of its partial fraction decomposition. We carry out an…
We show that there are finite monoids $M$ such that the Cartan matrix of the monoid algebra $\mathbb C M$ is non-singular, whilst the Cartan matrix of $kM$ is singular for some field $k$ of positive characteristic, disproving a recent…
We answer a question that was asked by Albert Baernstein II, regarding the coefficients of circular symmetrization. The conjecture is not true generically.
We present the long sought visual pattern in the Collatz problem with the aid of a logarithmic spiral. Using this newly discovered pattern, we show that the Collatz problem is linked to primes via Jacobsthal numbers. We then prove that no…
We prove a conjecture due to Y. Last on Jacobi matrices.
We study Deligne's conjecture on the monodromy weight filtration on the nearby cycles in the mixed characteristic case, and reduce it to the nondegeneracy of certain pairings in the semistable case. We also prove a related conjecture of…
The well-known Steinberg's conjecture asserts that any planar graph without 4- and 5-cycles is 3 colorable. In this note we have given a short algorithmic proof of this conjecture based on the spiral chains of planar graphs proposed in the…