For a simplicial complex ∆ we study the effect of barycentric subdivision on ring theoretic invariants of its StanleyReisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke and Herzog & Srinivasan, that relates the multiplicity of a standard graded k-algebra to the product of the maximal shifts in its minimal free resolution up to the ...

In [2], Billera proved that the R-algebra of continuous piecewise polynomial functions (C0 splines) on a d-dimensional simplicial complex 1 embedded in Rd is a quotient of the Stanley–Reisner ring A1 of 1. We derive a criterion to determine which elements of the Stanley–Reisner ring correspond to splines of higher-order smoothness. In [5], Lau and Stiller point out that the dimension of C k (1)...

We survey the Stanley-Reisner correspondence in combinatorial commutative algebra, describing fundamental applications involving Alexander duality, associated primes, f and h-vectors, and Betti numbers of monomial ideals.

It has been a privilege and an extraordinary learning opportunity to serve on the Law Committee's Subcommittee on Biomedical Ethics. Most especially, it has been a deeply rewarding experience to sit as one of the midwives attending the birth of these two superb papers on halakhic approaches to medical care for the terminally ill, the one by Rabbi Avram Reisner and the other by Rabbi Elliot Dorf...

In this thesis, we undertake a combinatorial study of certain aspects of triangulations of cartesian products of simplices, particularly in relation to their relevance in toric algebra and to their underlying product structure. The first chapter reports joint work with Samu Potka. The object of study is a class of homogeneous toric ideals called cut ideals of graphs, that were introduced by Stu...

ENWEndNote BIBJabRef, Mendeley RISPapers, Reference Manager, RefWorks, Zotero AMA Reisner P, Malukiewicz G. Diagnostics, classification and treatment of dry eye syndrome in the era COVID-19. Klinika Oczna / Acta Ophthalmologica Polonica. 2021;123(1):8-13. doi:10.5114/ko.2021.104746. APA Reisner, P., & Malukiewicz, (2021). Polonica, 123(1), 8-13. https://doi.org/10.5114/ko.2021.104746 Chicago Pa...

A thorough understanding of the dynamics of cirrus cloud formation is needed in order to parameterize these clouds accurately in numerical models. The scales at which cirrus clouds develop affect their treatment within the coarse resolution climate models, which typically have grid-point separations on The model used for this experiment is the non-hydrostatic verthe order of 200 km. There is a ...