We study a certain truncationA[n] of the ring of arithmetical functions with unitary convolution, consisting of functions vanishing on arguments > n. The truncations A[n] are artinian monomial quotients of a polynomial ring in finitely many indeterminates, and are isomorphic to the “artinified” Stanley-Reisner ring C[∆([n])] of a simplicial complex ∆([n]).

For a graph G, we show a theorem that establishes a correspondence between the fine Hilbert series of the Stanley-Reisner ring of the clique complex for the complementary graph of G and the fine subgraph polynomial of G. We obtain from this theorem some corollaries regarding the independent set complex and the matching complex.

A technique of minimal free resolutions of Stanley–Reisner rings enables us to show the following two results: (1) The 1-skeleton of a simplicial (d − 1)-sphere is d-connected, which was first proved by Barnette; (2) The comparability graph of a non-planar distributive lattice of rank d − 1 is d-connected.

In [22], Meyer and Reisner proved the Mahler conjecture for rovelution bodies. In this paper, using a new method, we prove that among origin-symmetric bodies of revolution in R 3 , cylinders have the minimal Mahler volume. Further, we prove that among parallel sections homothety bodies in R3 , 3-cubes have the minimal Mahler volume. Mathematics subject classification (2010): 52A10, 52A40.

It has long been recognized that tuberculous cavities may occur in the apex of the lower lobe of the lung, often known as the dorsal lobe (Kidd, 1886; Fowler, 1888 ; Sweany and others, 1931). Steen (1945) has reviewed the many publications on basal tuberculosis, but no paper I have traced has been concerned exclusively with tuberculous cavities of the dorsal lobe; most authors do not differenti...

We give a purely algebraic proof of the hypersurface case of the Toric Residue Mirror Conjecture recently proposed by Batyrev and Materov.

In this survey, we discuss two research areas related to Massey’s higher operations. The first direction is connected with the cohomology of Lie algebras and theory representations. second main theme at intersection toric topology, homotopy polyhedral products, homology local rings, Stanley–Reisner rings simplicial complexes.

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.