Face ring multiplicity via CM-connectivity sequences
نویسندگان
چکیده
The multiplicity conjecture of Herzog, Huneke, and Srinivasan is verified for the face rings of the following classes of simplicial complexes: matroid complexes, complexes of dimension one and two, and Gorenstein complexes of dimension at most four. The lower bound part of this conjecture is also established for the face rings of all doubly Cohen-Macaulay complexes whose 1-skeleton’s connectivity does not exceed the codimension plus one as well as for all (d− 1)-dimensional d-CohenMacaulay complexes. The main ingredient of the proofs is a new interpretation of the minimal shifts in the resolution of the face ring k[∆] via the Cohen-Macaulay connectivity of the skeletons of ∆.
منابع مشابه
Spongy Diamond
Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane was imagined. Further, the ide...
متن کاملTunable Control of Polyproline Helix (PPII) Structure via Aromatic Electronic Effects: An Electronic Switch of Polyproline Helix
Aromatic rings exhibit defined interactions via the unique aromatic π face. Aromatic amino acids interact favorably with proline residues via both the hydrophobic effect and aromatic-proline interactions, C-H/π interactions between the aromatic π face and proline ring C-H bonds. The canonical aromatic amino acids Trp, Tyr, and Phe strongly disfavor a polyproline helix (PPII) when they are prese...
متن کاملOn Rings with Small Hilbert{kunz Multiplicity
A result of Watanabe and Yoshida says that an unmixed local ring of positive characteristic is regular if and only if its Hilbert-Kunz multiplicity is one. We show that, for fixed p and d, there exist a number ǫ(d, p) > 0 such that any nonregular unmixed ring R its Hilbert-Kunz multiplicity is at least 1+ ǫ(d, p). We also show that local rings with sufficiently small Hilbert-Kunz multiplicity a...
متن کاملAn Automatic Method for Counting Annual Rings in Noisy Sawmill Images
What? A method to compute the number of annual rings in a log end face image. End faces are depicted in on-line sawmill production as the logs pass on a conveyor belt. The annual rings are analyzed in a region with a clear ring pattern, which is automatically detected. Why? The annual ring width on an end face is related to wood quality in the saw log, i.e., different ring widths represent wood...
متن کاملApplications of the Wavelet Multiplicity Function
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet connectivity problem.
متن کامل