A Note on the Composition of a Positive Integer whose Parts are Odd Integers

Abstract

In this study, we interested in the compostions of integers. Then the combinations of an integer whose each part is odd were examined. O_n = {(2a_1 + 1, ..., 2a_t + 1) : 2a_1 + 1 + ... + 2a_t + 1 = n and a_i positive integer} and we call the set as an odd combination set On set of an integer n . Then an action on the set are defined. Then the decomposition of the composition sets of a positive integer has been examined by using set theory. Then we also focused on the combination of an integer n whose sum is less than a fixed integer m. We have obtained the composition set of an integer whose largest part is less than m. Using these sets, we obtained recurrence relations.