Related papers: Conjecture of Wilf: a survey
Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with…
Crawford's et al. (2021) article on estimation of discrete choice models with unobserved or latent consideration sets, presents a unified framework to address the problem in practice by using "sufficient sets", defined as a combination of…
In his 1999 preprint "Universal Lie Algebra", P. Vogel put forward a hypothesis on the existence of a universal Lie algebra. Although this hypothesis remains open, it is known that many quantities in Lie theory admit universal descriptions.…
The union-closed sets conjecture, also known as Frankl's conjecture, is a well-studied problem with various formulations. In terms of lattices, the conjecture states that every finite lattice $L$ with more than one element contains a…
Nearly a decade ago, the science community was introduced to the $h$-index, a proposed statistical measure of the collective impact of the publications of any individual researcher. It is of course undeniable that any method of reducing a…
This is a survey paper presenting the history and both old and new results related to Kostant's problem. This problem asks for which modules over a semi-simple finite dimensional complex Lie algebra, the universal enveloping algebra…
The idea of calibrated recommendations is that the properties of the items that are suggested to users should match the distribution of their individual past preferences. Calibration techniques are therefore helpful to ensure that the…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
There has been an upsurge of interest in the consequences for quantum physics of the so-called Wigner's Friend Paradox. In its original formulation, the paradox has been turned inside out, and virtually every aspect of it has been looked…
This is the fourth of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It contains almost no new results. This time we…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…
The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to…
This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to a dangerous territory of the Riemann Hypothesis. We will mostly focus…
Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects…
Selection artefacts are common in science. A method of selecting samples from a larger population may produce bias, in either direction. It may induce correlations between variables independent in the full population, or mask correlations…
As science advances, the academic community has published millions of research papers. Researchers devote time and effort to search relevant manuscripts when writing a paper or simply to keep up with current research. In this paper, we…
Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's…
This is a survey of old and new problems and results in additive number theory.