Results 41 to 50 of about 6,993 (154)
Tubings, chord diagrams, and Dyson–Schwinger equations
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract We give series solutions to single insertion place propagator‐type systems of Dyson–Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a straightforward contribution.
Paul‐Hermann Balduf +5 more
wiley +1 more source
Obstructions to combinatorial formulas for plethysm
, 2018 Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples of $S^3(S^k)$ and $S^k(S^3)$, that these need not be counting functions of inhomogeneous polytopes of ...
Kahle, Thomas, Michalek, Mateusz
core +1 more source
On the variance of the mean width of random polytopes circumscribed around a convex body
Mathematika, Volume 70, Issue 4, October 2024.Abstract Let K$K$ be a convex body in Rd$\mathbb {R}^d$ in which a ball rolls freely and which slides freely in a ball. Let K(n)$K^{(n)}$ be the intersection of n$n$ i.i.d. random half‐spaces containing K$K$ chosen according to a certain prescribed probability distribution. We prove an asymptotic upper bound on the variance of the mean width of K(n)$K^{
Alexandra Bakó‐Szabó, Ferenc Fodor
wiley +1 more source
Polyhedral combinatorics of the
Discrete Applied Mathematics, 2016 The K-partitioning problem consists in partitioning the vertices of a weighted graph in K sets in order to minimize a function related to the edge weights. We introduce a linear mixed integer formulation with edge variables and representative variables. We investigate the polyhedral combinatorics of the problem, study several families of facet-defining
Alès, Zacharie +2 more
openaire +4 more sources
Mathematika, Volume 70, Issue 4, October 2024.Abstract We extend classical estimates for the vector balancing constant of Rd$\mathbb {R}^d$ equipped with the Euclidean and the maximum norms proved in the 1980s by showing that for p=2$p =2$ and p=∞$p=\infty$, given vector families V1,…,Vn⊂Bpd$V_1, \ldots , V_n \subset B_p^d$ with 0∈∑i=1nconvVi$0 \in \sum _{i=1}^n \mathrm{conv}\,V_i$, one may select
Gergely Ambrus, Rainie Bozzai
wiley +1 more source
Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.Abstract Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$, the m$m$‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$. The classical Shi arrangement (m=0$m=0$) was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for W$W$.
Matthew Dyer +3 more
wiley +1 more source
Polyhedral geometry and combinatorics of an autocatalytic ecosystem
Journal of Mathematical ChemistryDeveloping a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about
Gagrani, Praful +3 more
openaire +2 more sources
Arithmetic of marked order polytopes, monotone triangle reciprocity, and partial colorings [PDF]
, 2013 For a poset P, a subposet A, and an order preserving map F from A into the real numbers, the marked order polytope parametrizes the order preserving extensions of F to P.
Jochemko, Katharina, Sanyal, Raman
core
Fundamental polytopes of metric trees via parallel connections of matroids
, 2019 We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like
Delucchi, Emanuele, Hoessly, Linard
core
Discrete Yamabe Problem for Polyhedral Surfaces. [PDF]
Discrete Comput Geom, 2023 Dal Poz Kouřimská H.
europepmc +1 more source