Rippling is a technique developed for inductive theorem proving which uses syntactic diierences of terms to guide the proof search. Annotations (like colors) to terms are used to maintain this information. This technique has several advantages, e.g. it is highly goal oriented and involves little search. In this paper we give a general formalisation of coloring terms in a higher-order setting. W...

We generalize Björner and Stanley’s poset of compositions to m-colored compositions. Their work draws many analogies between their (1-colored) composition poset and Young’s lattice of partitions, including links to (quasi-)symmetric functions and representation theory. Here we show that many of these analogies hold for any number of colors. While many of the proofs for Björner and Stanley’s pos...

The structure of edge-colored complete graphs containing no properly colored triangles has been characterized by Gallai back in the 1960s. More recently, Cǎda et al. and Fujita independently determined bipartite C 4 . We characterize even cycles, or equivalently, without a 6 In particular, we first deal with simple case 2-edge-colored graphs, using result Yeo. Next, for k ≥ 3, define four class...

introduction: microleakage is a major factor affecting the longevity of adhesive restorations. colored compomer is a new restorative material that was specifically designed for the restoration of primary molars in different colors, but their microleakage is unknown. this study was carried out to compare the microleakage of a colored compomer (twinky star) and a conventional compomer (f2000) wit...