Bimonotone enumeration

Bimonotone enumeration

Solutions of a diophantine equation f(a, b) = g(c, d), with a, b, c, d in some finite range, can be efficiently enumerated by sorting the values of f and g in ascending order and searching for collisions. This article considers functions f : N×N → Z that are bimonotone in the sense that f(a, b) ≤ f(a′, b′) whenever a ≤ a′ and b ≤ b′. A two-variable polynomial with non-negative coefficients is a...

Enumeration of Enumeration Algorithms

In this paper, we enumerate enumeration problems and algorithms. Other useful catalogues for enumeration algorithms are provided by Komei Fukuda and Yasuko Matsui. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.

Enumeration Workshop

Sequence enumeration

The purpose of this paper is to present a method for treating uniformly a large number of enumeration problems involving sequences over a finite alphabet subject to general restrictions. Many of these problems are classical in origin, including the Mrnage problem (Lucas [16]), the alternating permutation problem (Netto [19], Andr6 [1, 2]), the derangement problem (Montmort [18]), and more recen...

Algebraic Enumeration