Related papers: Sagan numbers
The exact composition of a specific class of compact stars, historically referred to as "neutron stars", is still quite unknown. Possibilities ranging from hadronic to quark degrees of freedom, including self-bound versions of the latter…
In this paper, we study the combinatorial structures of straight and ordinary m\'enage permutations. Based on these structures, we prove four formulas. The first two formulas define a relationship between the m\'enage numbers and the…
A number of the form $x(x+1)/2$ where $x$ is an integer is called a triangular number. Suppose, $N(a_1,\cdots,a_k;n)$ and $T(a_1,\cdots,a_k;n)$ denote the number of ways $n$ can be expressed as $\sum_{i=1}^k a_ix_i^2$ and $\sum_{i=1}^k…
This paper is devoted to the study of particular geometrically defined intersection classes of graphs. Those were previously studied by Magnant and Martin, who proved that these graphs have arbitrary large chromatic number, while being…
We introduce the notion of numerical semigroups generated by concatenation of arithmetic sequences and show that this class of numerical semigroups exhibit multiple interesting behaviours.
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
This is a detailed and self-contained introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios as presented in Book V of…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
Sequences whose terms are equal to the number of functions with specified properties are considered. Properties are based on the notion of derangements in a more general sense. Several sequences which generalize the standard notion of…
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several…
Much progress has been made on the problem of calculating $g(n)$ for various classes of integers $n$, where $g$ is the group-counting function. We approach the inverse problem of solving the equations $g(n) = 6$ and $g(n) = 7$ in $n$. The…
Forcing was first introduced by Paul J. Cohen in his work on the independence of the Continuum Hypothesis. Other formulations of forcing appeared using Model Theory, Boolean-valued Models, and Topos Theory. There is a folkloric claim that…
Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers- equations made of…
In the middle of the third millennium BC the Sumerians must have noticed that the reciprocal of the number 7,in contrast to the numbers 1,2,3,4,5,and 6,could not be expressed by a finite sexagesimal fraction but it recurred every three…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $1/9 = 11.11%$ for each digit from 1 to 9. This is by no means the case, and one can…
Arising out of an attempt at a new foundations of mathematics, in which relations are more primitive than sets, and out of the theoretical physicists' concept of underlying causes of empirical phenomena, the idea of a purely mathematical…
In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.