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

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.