相关论文: Coloring complexes and arrangements
We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as…
We investigate the complexity of generalizations of colourings (acyclic colourings, $(k,\ell)$-colourings, homomorphisms, and matrix partitions), for the class of transitive digraphs. Even though transitive digraphs are nicely structured,…
List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…
We give an explicit expression for the contact loci of hyperplane arrangements and show that their cohomology rings are combinatorial invariants. We also give an expression for the restricted contact loci in terms of Milnor fibers of…
In this paper, we consider multivariate hyperedge elimination polynomials and multivariate chromatic polynomials for hypergraphs. The first set of polynomials is defined in terms of a deletion-contraction-extraction recurrence, previously…
A superdiagonal composition is one in which the $i$-th part or summand is of size greater than or equal to $i$. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In…
We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated…
Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement graphs of simple great-circle arrangements have chromatic number at most $3$. Motivated by this conjecture, we study the colorability of arrangement graphs for different…
There is a natural one-to-one correspondence between squarefree monomial ideals and finite simple hypergraphs via the cover ideal construction. Let H be a finite simple hypergraph, and let J = J(H) be its cover ideal in a polynomial ring R.…
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
In this paper we give convex-ear decompositions for the order complexes of several classes of posets, namely supersolvable lattices with non-zero Mobius functions and rank-selected subposets of such lattices, rank-selected geometric…
We construct $S^r$-colored knot Floer homologies and prove that they satisfy categorified recurrence relations. The associated Euler characteristic implies $q$-holonomicity of the corresponding sequence of colored Alexander polynomials, in…
In this work, we continue the study of vertex colorings of graphs, in which adjacent vertices are allowed to be of the same color as long as each monochromatic connected component is of relatively small cardinality. We focus on colorings…
Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and…
Coloured Alexander polynomials form a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group $U_q(sl(2))$ at roots of unity. This sequence recovers the original Alexander polynomial as the…
The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices into two parts, the second one by a…
We inductively define layers of colorings of knot and knotted surface diagrams using ternary quasigroups. Homological invariants from such systems of colorings use shorter differentials and of higher degree than the standard homology…
The orbital bivariate chromatic polynomial, introduced in this article, counts the number of ways to color the vertices of a graph with $\lambda$ colors such that adjacent vertices either receive distinct colors from a set of $\lambda$…
Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B…