Abstract: Partition functions and graph polynomials have found many applications in combinatorics, physics, biology and even the mathematics of finance. Studying their complexity poses some problems.

👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear ...

👉 Learn how to determine the end behavior of a polynomial function from the graph of the function. To do this we look at the endpoints of the graph to see if it rises or falls as the value of x ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of the recent work by ...

Abstract: The construction of spectral filters for graph wavelet transforms is addressed in this paper. Both the undecimated and decimated cases will be considered. The filter functions are ...

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\[f(x) = x^{-2}\text{ or }f(x) = \frac{1}{x^{2}}\] Both functions have asymptotes at \(x = 0\) and \(y = 0\) for their basic forms. The vertical asymptote at \(x = 0 ...

We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers–Wannier duality can be derived from the Tutte ...

A holy grail of theoretical computer science, with numerous fundamental implications to more applied areas of computing such as operations research and artificial intelligence, is the question of ...