Partitions modulo image and circulant matrices Original Research Article

This paper is about a connection between a general problem of partitions in image and the expression of determinants of certain circulant matrices. The main result of the article is a method for calculating, in certain special cases, explicit formulas for the number of partitions of elements in image in distinct summands and the number of partitions of elements in image with less than t repetitions. Explicit formulas for partitions in image in the general case can be found by explicitly calculating the determinants of certain circulant matrices.