We present new, simple proofs for the enumeration of ve of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation, using combinatorial arguments. The previous proofs of these four cases were quite complicated. For one more symmetry class we give an elementary proof in the case when two of the sides of the box are equa...

When the partitions of [n] = {1, 2, . . . , n} are identified with the restricted growth functions on [n], under a known bijection, certain enumeration problems for classical word statistics are formulated for set partitions. In this paper we undertake the enumeration of partitions of [n] with respect to the number of occurrences of rises, levels and descents, of arbitrary integral length not e...

A (convex) polytope P is said to be 2-level if for every direction of hyperplanes which is facet-defining for P , the vertices of P can be covered with two hyperplanes of that direction. The study of these polytopes is motivated by questions in combinatorial optimization and communication complexity, among others. In this paper, we present the first algorithm for enumerating all combinatorial t...

In this paper we present three algorithms that solve three combinatorial optimization problems related to each other. One of them is the patience sorting game, invented as a practical method of sorting real decks of cards. The second problem is computing the longest monotone increasing subsequence of the given sequence of n positive integers in the range 1, . . . , n. The third problem is to en...

Most indirect hexahedral meshing methods rely on 10 patterns of subdivision of the hexahedron into tetrahedra. A recent observation at least one more pattern exists raise the question of the actual number of subdivisions of the hexahedron into tetrahedra. In this article answers we enumerate these subdivisions by exhausting all possible ways to combine tetrahedra into hexahedra. We introduce a ...

In this paper we present three algorithms that solve three combinatorial optimization problems related to each other. One of them is the patience sorting game, invented as a practical method of sorting real decks of cards. The second problem is computing the longest monotone increasing subsequence of the given sequence of n positive integers in the range 1; : : : ; n. The third problem is to en...

ZRAM is a software library which renders the power of parallel computers usable for combinatorial optimization and enumeration. It provides a set of parallel search engines for branch-and-bound, reverse search, backtrack¬ ing and tree-size estimation. These search engines hide the complexity of parallelism from the application programmer. ZRAM contains the first parallel implementation of the r...

We extend the original cylinder conjecture on point sets in affine three-dimensional space to more general framework of divisible linear codes over $\mathbb{F}_q$ and their classification. Through a mix programming, combinatorial techniques computer enumeration, we investigate structural properties these codes. In this way, can prove reduction theorem for generalization conjecture, show some in...

In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in the tree can get multiple labels. For all tree classes we show characterizations of suitable generating functions for the tree enumeration sequence via diff...