Set families with a forbidden subposet.
Set partitions with successions and separations.
Set systems with restricted -wise intersections modulo prime powers.
Set theoretical analogues of two combinatorial theorems
Set vertex colorings and joins of graphs
For a nontrivial connected graph , let be a vertex coloring of where adjacent vertices may be colored the same. For a vertex of , the neighborhood color set is the set of colors of the neighbors of . The coloring is called a set coloring if for every pair of adjacent vertices of . The minimum number of colors required of such a coloring is called the set chromatic number . A study is made of the set chromatic number of the join of two graphs and . Sharp lower and upper bounds...
Set-polynomials and polynomial extension of the Hales-Jewett theorem.
Sets in the plane with many concyclic subsets.
Sets, lists and noncrossing partitions.
Sets of parts such that the partition function is even
Sets of points determining only acute angles and some related colouring problems.
Sets with two associative operations
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
Set-systems with restricted multiple intersections.
Several generating functions for second-order recurrence sequences.
Several -series identities from the Euler expansions of and
In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two -series identities obtained by the Euler expansions of and . Several -series identities are obtained involving a -series identity in Ramanujan’s Lost Notebook.
Several results on chordal bipartite graphs
The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that,...
S-functions and characters of Lie algebras and Lie groups
Shadow trees of Mandelbrot sets
The topology and combinatorial structure of the Mandelbrot set (of degree d ≥ 2) can be studied using symbolic dynamics. Each parameter is mapped to a kneading sequence, or equivalently, an internal address; but not every such sequence is realized by a parameter in . Thus the abstract Mandelbrot set is a subspace of a larger, partially ordered symbol space, . In this paper we find an algorithm to construct “visible trees” from symbolic sequences which works whether or not the sequence is realized....
Shadows of colored complexes.
Shape tiling.
Shape-Wilf-ordering on permutations of length 3.