Related papers: Cassels bases
This note is a response to one of problems posed by A.K. Kwasniewski in one of his recent papers. Namely for the sequence of finite cobweb subposets, the looked for explicit formulas for corresponding sequence of characteristic polynomials…
Previous research on exceptional units has primarily focused on the ring of rational integers or abstract finite rings, often restricted to linear or quadratic constraints. In this paper, we extend the concept of polynomial-type exceptional…
We give an almost entirely model-theoretic account of both Ramsey classes of finite structures and of generalized indiscernibles as studied in special cases in (for example) [7], [9]. We understand "theories of indiscernibles" to be special…
Following ideas from [14], we give a uniform large genus asymptotics for primitive psi-class intersection numbers on the moduli space of stable algebraic curves, and extend this result including insertions of zeros in a certain uniform way.…
We prove an asymptotic formula for the number of integral points of bounded log anticanonical height on a singular quartic del Pezzo surface over arbitrary number fields, with respect to the largest admissible boundary divisor. The…
We present proofs of the basic isopermetric structure theory, obtaining some new simplified proofs. As an application, we obtain simple descriptions for subsets $S$ of an abelian group with $|kS|\le k|S|-k+1$ or $|kS-rS|- (k+r)|S|,$ where…
The concept of additive basis has been investigated in the literature for several mathematicians which works with number theorem. Recently, the concept of finitely stable additive basis was introduced. In this note we provide a…
Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer…
We consider simplicial polytopes, and more general simplicial complexes, without missing faces above a fixed dimension. Sharp analogues of McMullen's generalized lower bounds, and of Barnette's lower bounds, are conjectured for these…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer can be represented as the sum of $h$ integers (not necessarily distinct) of $A$. An asymptotic basis $A$ of order $h$ is minimal if no…
This paper develops a general theory of canonical bases, and how they arise naturally in the context of categorification. As an application, we show that Lusztig's canonical basis in the whole quantized universal enveloping algebra is given…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…
The set A = {a_n} of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If a_n ~ alpha n^h for some real number alpha > 0, then alpha is called an…
Almost forty years ago, C.T.C. Wall systematically analyzed the set of "thickenings" of a finite CW complex. Of the results he obtained, probably the most computationally important is the "suspension theorem," which is an exact sequence…
We revisit the classical problem of construction of a fundamental system of solutions to a linear ODE whose elements remain analytic and linearly independent for all values of the roots of the characteristic polynomial.
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
Erd\"os conjectured the existence of an infinite Sidon sequence of positive integers which is also an asymptotic basis of order 3. We make progress towards this conjecture in several directions. First we prove the conjecture for all cyclic…
In earlier work, we introduced three families of polynomials where the generating function of each set includes one of the three Jackson $q$-analogs of the Bessel function. This paper gives determinant representation for each family, their…