In this work labeling of planar graphs is taken up which involves labeling the p vertices, the q edges and the f internal faces such that the weights of the faces form an arithmetic progression with common difference d. If d = 0, then the planar graph is said to have an Inner Magic labeling; and if d = 0, then it is Inner Antimagic labeling. Some new kinds of graphs have been developed which ha...

We present core data structures and algorithms for matching graph patterns with general recursion. Our approach uses magic sets, a well-known technique from deductive databases, which combines fixpoint-based bottom-up query evaluation with top-down handling of input parameters. Furthermore, this technique is enhanced with the global search plans, thus non-recursive calls are always flattened be...

A magic square of order n is an n by n matrix with distinct nonnegative integer entries such that every row sum, column sum, and (two) diagonal sums equals to the same number m, the magic number. Adding 1 to every entry will give us a traditional magic square of positive integers. A magic square is pure if the entries are the consecutive numbers from 0 to n − 1, and hence it has magic number 3 ...

We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart’s theory of lattice-point counting to a convex pol...

When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of most external path does not affect curve. We strengthen this statement and also make it more concrete by observing factorization property: if $Z^{}_{n+k}$ denotes refined partition function system $n+k$ non-crossing paths, with endpoints $k$ paths possibly displaced, then at...

Network is a powerful language to represent relational data. One way to understand network is to analyze groups of nodes which share same properties or functions. The task of discovering such groups is known as community detection. Generally, two types of information can be utilized to fulfill this task, i.e., the link structures and the node attributes. The temporal text network is a special k...

A good compiler which implements many optimizations during its compilation phases must be able to perform several static analysis techniques such as control flow or data flow analysis. Besides compilers, these techniques are common for static analyzers as well to retrieve information from source code, for example for code auditing, quality assurance or testing purposes. Implementing control flo...