Related papers: On partitions avoiding right crossings
We give the first analysis of the computational complexity of {\it coalition structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a valuation function $v:2^N\rightarrow\RR$ over the subsets of nodes, the problem is to…
Integer partitions are one of the most fundamental objects of combinatorics (and number theory), and so is enumerating objects avoiding patterns. In the present paper we describe two approaches for the systematic counting of classes of…
Many papers have studied inequalities for partition functions. Recently, a number of papers have considered mixtures between additive and multiplicative behavior in such inequalities. In particular, Chern-Fu-Tang and Heim-Neuhauser gave…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
In this paper we study generating functions resembling the rank of strongly unimodal sequences. We give combinatorial interpretations, identities in terms of mock modular forms, asymptotics, and a parity result. Our functions imitate a…
We show that permutations avoiding both of the (classical) patterns 4321 and 3241 have the algebraic generating function conjectured by Vladimir Kruchinin.
The generating functional is suggested for multiparticle generation processes. In mean field approximation of high density QCD two equations for new generating functional are derived: linear functional equation for an arbitrary initial…
A preferential arrangement of a set $X_n=\{1,2,...,n\}$ is an ordered partition of the set $X_n$ induced with a linear order. Separation of blocks of a preferential arrangement with bars result in the notation of barred preferential…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that…
In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels…
We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By…
We study generating functions which count the sizes of $t$-cores of partitions, and, more generally, the sizes of higher rows in $t$-core towers. We then use these results to derive an asymptotic for the average size of the $t$-defect of…
A non-crossing pairing on a bitstring matches 1s and 0s in a manner such that the pairing diagram is nonintersecting. By considering such pairings on arbitrary bitstrings $1^{n_1} 0^{m_1} ... 1^{n_r} 0^{m_r}$, we generalize classical…