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44  Articles
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We present a bijective proof of Shapiro's convolution formula involving Catalan numbers of even index. As a corollary, we give a new interpretation of the Catalan numbers.

In this paper, we present a novel method to construct cryptographically strong bijective substitution-boxes based on the complicated dynamics of a new hyperchaotic system. The new hyperchaotic system was found to have good characteristics when compared wi... see more

Context-awareness is becoming a key aspect of mobile learning systems. In fact, an efficient mobile learning system has to be sensitive to the context that characterizes the interactions between humans, applications and the surrounding environment. Resear... see more

Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been found so far. In t... see more

Based on the combinatorial proof of Schur's partition theorem given by Bressoud, and the combinatorial proof of Alladi's partition theorem given by Padmavathamma, Raghavendra and Chandrashekara, we obtain a bijective proof of a partition theorem of Alladi... see more

A simple graph G(V, E) admits an H-covering if every edge in G belongs to a subgraph of G isomorphic to H. In this case, G is called H-magic if there exists a bijective function f : V ? E ? {1, 2... see more

Let G = (V(G),E(G)) be a graph with the nonempty vertex set V(G) and the edge set E(G). Let Zn be the group of integers modulo n and let k be a positive integer. A modular irregular labeling of a grap... see more

Let LL be an algebra over a field FF with the binary operations ++ and [,][,]. Then LL is called a left Leibniz algebra if it satisfies the left Leibniz identity: [[a,b],c]=[a,[b,c]]-[b,[a,c]][[a,b],c]=[a,[b,c]]-[b,[a,c]] for all elements a,b,c?La,b,c\in ... see more


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