Research: Some Reasons for the Grades We Give Compositions

Does Rationality Give Us Reasons?

Most of us take it for granted that we ought to be rational—to have the bundle of dispositions and abilities that constitute the faculty of rationality. Most of us also take it for granted that we ought to satisfy various individual requirements of rationality: we ought not to believe it is Monday and also believe it is not Monday; we ought to intend to catch the 12.50, if we intend to get to a...

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...

Some Inplace Identities for Integer Compositions

In this paper, we give two new identities for compositions, or ordered partitions, of integers. These two identities are based on closely-related integer partition functions which have recently been studied. Thanks to the structure inherent in integer compositions, we are also able to extensively generalize both of these identities. Bijective proofs are given and generating functions are provid...

Some reasons for generalising domain theory

One natural way to generalize Domain Theory is to replace partially ordered sets by categories. This kind of generalization has recently found application in the study of concurrency. An outline is given of the elegant mathematical foundations which have been developed. This is specialized to give a construction of cartesian closed categories of domains, which throws light on standard presentat...

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