Restricted color $n$-color compositions

Some n-Color Compositions

In the classical theory of partitions, compositions were first defined by MacMahon [1] as ordered partitions. For example, there are 5 partitions and 8 compositions of 4. The partitions are 4, 31, 22, 21, 1 and the compositions are 4, 31, 13, 22, 21, 121, 12, 1. Agarwal and Andrews [2] defined an n-color partition as a partition in which a part of size n can come in n different colors. They den...

n-Color Odd Self-Inverse Compositions

An n-color odd self-inverse composition is an n-color self-inverse composition with odd parts. In this paper, we obtain generating functions, explicit formulas, and recurrence formulas for n-color odd self-inverse compositions.

N-color Ashkin-Teller model

shows nonuniversal critical behavior in two dimensions in the neighborhood of K4 =0. To see if this behavior persists for N & 2 we perform a first-order-perturbation expansion around the decoupling point in two dimensions. As an aid in interpreting the results of this perturbation expansion we have determined the phase diagram of the system through mean-field theory and Monte Carlo studies in 1...

Iranian's color emotional dimensions

S-Restricted Compositions Revisited

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed-form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to...