Tight combinatorial manifolds and graded Betti numbers

DOI10.1007/s13348-015-0137-zzbMath1409.13041OpenAlexW1977811461MaRDI QIDQ495984

Satoshi Murai

Publication date: 16 September 2015

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13348-015-0137-z

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Triangulating manifolds (57Q15) Syzygies, resolutions, complexes and commutative rings (13D02) Combinatorial aspects of simplicial complexes (05E45)

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Cites Work

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• On the generalized lower bound conjecture for polytopes and spheres
• An infinite family of tight triangulations of manifolds
• Separation index of graphs and stacked 2-spheres
• The mu vector, Morse inequalities and a generalized lower bound theorem for locally tame combinatorial manifolds
• A necessary condition for the tightness of odd-dimensional combinatorial manifolds
• Stacked polytopes and tight triangulations of manifolds
• Rigidity and the lower bound theorem. I
• Deformation classes of graded modules and maximal Betti numbers
• Minimal resolutions of some monomial ideals
• \(f\)-vectors of 3-manifolds
• Socles of Buchsbaum modules, complexes and posets
• Lower-bound theorems for pseudomanifolds
• Computation of Betti numbers of monomial ideals associated with stacked polytopes
• Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers.
• Combinatorial manifolds with few vertices
• Tight polyhedral submanifolds and tight triangulations
• Combinatorics and commutative algebra.
• Regularity 3 in edge ideals associated to bipartite graphs
• On \(r\)-stacked triangulated manifolds
• Subadditivity of syzygies of Koszul algebras
• A tightness criterion for homology manifolds with or without boundary
• Applications of Klee's Dehn-Sommerville relations
• On stacked triangulated manifolds
• On stellated spheres and a tightness criterion for combinatorial manifolds
• The minimum number of vertices of a simple polytope
• A proof of the lower bound conjecture for convex polytopes
• Face numbers of pseudomanifolds with isolated singularities
• A note on the subadditivity problem for maximal shifts in free resolutions
• Lectures on Polytopes
• Monomial Ideals
• Upper bounds for the betti numbers of a given hilbert function
• Maximum betti numbers of homogeneous ideals with a given hilbert function
• A census of tight triangulations

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