Related papers: Generalised Barred Preferential Arrangements
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
We study the structure of combinatorial Burnside groups, which receive equivariant birational invariants of actions of finite groups on algebraic varieties.
Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…
We introduce information bearing systems (IBRS) as an abstraction of many logical systems. We define a general semantics for IBRS, and show that IBRS generalize in a natural way preferential semantics and solve open representation problems.
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…
In these notes we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
We introduce a constrained priority mechanism that combines outcome-based matching from machine-learning with preference-based allocation schemes common in market design. Using real-world data, we illustrate how our mechanism could be…
Preferential equality is an equivalence relation on fuzzy subsets of finite sets and is a generalization of classical equality of subsets. In this paper we introduce a tightened version of the preferential equality on fuzzy subsets and…
An urn contains balls of d colors. At each time, a ball is drawn and then replaced together with a random number of balls of the same color. Assuming that some colors are dominated by others, we prove central limit theorems. Some…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
Given a periodic graph, we wish to determine via combinatorial methods whether it has periodic embeddings in the plane that -- via motions that preserve edge-lengths and periodicity -- can be continuously deformed into another non-congruent…
We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
We discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives ($A,B,C$) we reduce the $(3!)^3 = 216$ possible…
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…