On permutation polynomials over finite fields.
On permutations generated by infinite binary words.
On permutations in bipartite graphs
On permutations involving pairs of twins.
On permutographs
On planar mixed hypergraphs.
On planarity of graphs in 3-manifolds.
On plethysm conjectures of Stanley and Foulkes: the case.
On polynomial time decidability of induced-minor-closed classes
On polynomials of Sheffer type arising from a Cauchy problem.
On potentially -graphic sequences
For given a graph , a graphic sequence is said to be potentially -graphic if there is a realization of containing as a subgraph. In this paper, we characterize the potentially -positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence to be potentially -graphic, where is a complete graph on vertices and is a graph obtained from by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for...
On potentially -graphic sequences
Let be the graph obtained from by removing the edges set of where is a subgraph of . In this paper, we characterize the potentially and -graphic sequences where is a tree on 5 vertices and 3 leaves.
On potentially nilpotent double star sign patterns
A matrix whose entries come from the set is called a sign pattern matrix, or sign pattern. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by , is introduced. We determine all potentially nilpotent sign patterns in and , and prove that one sign pattern in is potentially stable.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On powers of 2 dividing the values of certain plane partition functions.
On powers of non-negative matrices
On P-polynomial representations of projective geometries in algebraic combinatorial geometries.
On prime and principal ideals on graphs
On prime factors of sums of integers III
On prime labeling of union of tadpole graphs
A graph of order is said to be a prime graph if its vertices can be labeled with the first positive integers in such a way that the labels of any two adjacent vertices in are relatively prime. If such a labeling on exists then it is called a prime labeling. In this paper we seek prime labeling for union of tadpole graphs. We derive a necessary condition for the existence of prime labelings of graphs that are union of tadpole graphs and further show that the condition is also sufficient...