We study the Mathias--Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias--Prikry forcings with summable ideals are all mutually bi-embeddable....
We give completely combinatorial proofs of the main results of [3] using polygons. Namely, we prove that the mapping class group of a surface with boundary acts faithfully on a finitely-generated linear category. Along the way we prove some foundatio...
We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an understanding of how t...
Paisley is a declarative lightweight embedded domain-specific language for expressive, non-deterministic, non-invasive pattern matching on arbitrary data structures in Java applications. As such, it comes as a pure Java library of pattern-matching co...
Visualizing an outfit is an essential part of shopping for clothes. Due to the combinatorial aspect of combining fashion articles, the available images are limited to a pre-determined set of outfits. In this paper, we broaden these visualizations by...
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the variables o...
Answer Set Programming (ASP) is a powerful modelling formalism that is very efficient in solving combinatorial problems. ASP solvers implement the stable model semantics that eliminates circular derivations between Boolean variables from the solution...
Recently, Clow and McKay proved that the Digraph Placement ruleset is universal for normal play: for all normal play combinatorial games $X$, there is a Digraph Placement game $G$ with $G=X$. Clow and McKay also showed that the 22 game values born by...
In the combinatorial-action contract model (Dütting et al., FOCS'21) a principal delegates the execution of a complex project to an agent, who can choose any subset from a given set of actions. Each set of actions incurs a cost to the agent, given b...
Combinatorial Objects Generators for Java 7+. (⭐ 92)
This article, based on joint work with Gabriel Carroll, Andy Itsara, Ian Le, Gregg Musiker, Gregory Price, Dylan Thurston, and Rui Viana, presents a combinatorial model based on perfect matchings that explains the symmetries of the numerical arrays t...
Efficient, functional algorithms for generating lazy sequences for common combinatorial functions (⭐ 358)
I suppose the entire premise of this question will probably seem really naive to... combinatoricians? combinatoricists? combinatorialists? but I've been thinking recently that a lot of the math topics...
Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the classical to...
Combinatorial objects stream generators for Java. (⭐ 192)
combinatorics" was introduced in the late 1970s. Through the early or mid-1990s, typical combinatorial objects of interest in algebraic combinatorics
We propose a computational, convex hull free framework that takes advantage of the combinatorial structure of a zonotope, as for example its symmetry group, to orbitwise generate all canonical representatives of its vertices. We illustrate the propos...
Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place $k^\ell$ chips o...
Chip-firing is a combinatorial game played on a graph, in which chips are placed and dispersed on the vertices until a stable configuration is achieved. We study a chip-firing variant on an infinite, rooted directed $k$-ary tree, where we place $k^n$...
A general lattice theoretic construction of Reading constructs Hopf subalgebras of the Malvenuto-Reutenauer Hopf algebra (MR) of permutations. The products and coproducts of these Hopf subalgebras are defined extrinsically in terms of the embedding i...