scholarly journals Nearly Neighbourly Families of Standard Boxes

10.37236/6771 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Jacek Bojarski ◽  
Andrzej Piotr Kisielewicz ◽  
Krzysztof Przesławski
Keyword(s):  
Combinatorial Classification

It is shown that each nearly neighbourly family of standard boxes in $\mathbb{R}^3$ has at most 12 elements. A combinatorial classification of all such families that have exactly 12 elements is given. All the families satisfying an extra property called incompressibility are described. Compressible families are discussed briefly.

scholarly journals Multiplicity-Free Schubert Calculus

2010 ◽  
Vol 53 (1) ◽  
pp. 171-186 ◽  
Author(s):  
Hugh Thomas ◽  
Alexander Yong
Keyword(s):  
Algebraic Geometry ◽  
Schubert Calculus ◽  
Chow Ring ◽  
Free Products ◽  
Linear Basis ◽  
Combinatorial Classification ◽  
Schubert Classes ◽  
Multiplicity Free

AbstractMultiplicity-free algebraic geometry is the study of subvarieties Y ⊆ X with the “smallest invariants” as witnessed by a multiplicity-free Chow ring decomposition of [Y] ∈ A*(X) into a predetermined linear basis.This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis. We give a nonrecursive combinatorial classification of multiplicity-free Richardson varieties, i.e., we classify multiplicity-free products of Schubert classes. This answers a question of W. Fulton.

scholarly journals Combinatorial classification of quantum lens spaces

2018 ◽  
Vol 297 (2) ◽  
pp. 339-365
Author(s):  
Peter Jensen ◽  
Frederik Klausen ◽  
Peter Rasmussen
Keyword(s):  
Lens Spaces ◽  
Combinatorial Classification

Quadratic-monomial generated domains from mixed signed, directed graphs

2019 ◽  
Vol 29 (02) ◽  
pp. 279-308
Author(s):  
Michael A. Burr ◽  
Drew J. Lipman
Keyword(s):  
Directed Graphs ◽  
Complete Characterization ◽  
Combinatorial Structure ◽  
Signed Directed Graph ◽  
Odd Cycle ◽  
Combinatorial Classification ◽  
Special Case ◽  
Text Condition

Determining whether an arbitrary subring [Formula: see text] of [Formula: see text] is a normal or Cohen-Macaulay domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. We provide a complete characterization of the normality, normalizations, and Serre’s [Formula: see text] condition for quadratic-monomial generated domains. For a quadratic-monomial generated domain [Formula: see text], we develop a combinatorial structure that assigns, to each quadratic monomial of the ring, an edge in a mixed signed, directed graph [Formula: see text], i.e. a graph with signed edges and directed edges. We classify the normality and the normalizations of such rings in terms of a generalization of the combinatorial odd cycle condition on [Formula: see text]. We also generalize and simplify a combinatorial classification of Serre’s [Formula: see text] condition for such rings and construct non-Cohen–Macaulay rings.

scholarly journals Combinatorial classification of piecewise hereditary algebras

2011 ◽  
Vol 23 (6) ◽  
Author(s):  
Marcelo Lanzilotta ◽  
Maria Julia Redondo ◽  
Rachel Taillefer
Keyword(s):  
Combinatorial Classification ◽  
Hereditary Algebras

A combinatorial classification of finite quasigroups

2017 ◽  
Vol 57 (6) ◽  
pp. 711-732
Author(s):  
I. P. Mishutushkin
Keyword(s):  
Combinatorial Classification
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