The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give an algebraic combinatorics formula for the Möbius transform of an abstract simplicial complex K on [m] = {1, . . . ,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound o...

This paper addresses the problem of characterizing the possible h-vectors of a matroid complex ∆. We define the h-vector in Section 1, both in terms of the f -vector, and as the dimension vector of a graded ring S(∆) which is given as the Stanley-Reisner ring of ∆ modulo a linear system of parameters. Section 1 ends with a brief survey of the literature on h-vectors of matroid complexes. In Sec...

The notion of strict closedness rings was given by J. Lipman [Amer. Math. 93 (1971), pp. 649–685] in connection with a conjecture O. Zariski. present purpose is to give practical method construction strictly closed rings. It also shown that the Stanley-Reisner simplicial complexes (resp. $F$-pure satisfying condition $(\operatorname {S}_2)$ Serre) are weakly Arf)

Adviser: Carina Curto Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How d...

This paper was adopted by the CJLS on December 12, 1990 by a vote of eleven in favor, two opposed, and five abstaining ( 11-2-5). Members voting in favor: Rabbis Kassel Abelson, Ben Zion Bergman, Elliot N. Dorff, Amy Eilberg, Dov Peretz Elkins, Howard Handler, Reuven Kimelman, Lionel E. Moses, Mayer E. Rabinowitz, Joel Rembaum, Morris M. Shapiro. Members voting against: Rabbis Avram I. Reisner ...

This paper was adopted by the CJLS on December 12, 1990 by a vote of thirteen infavor, one opposed, andfour abstaining (13-1-4). Members voting in favor: Rabbis Ben Zion Bergman, Stanley Bramnick, Jerome M. Epstein, David M. Feldman, Sam Fraint, Howard Handler, Reuven Kimelman, Herbert Mandl, Lionel E. Moses, Mayer E. Rabinowitz, Avram I. Reisner, Joel Rembaum, Joel Roth. Member voting against:...

A weaker form of the multiplicity conjecture of Herzog, Huneke, and Srinivasan is proven for two classes of monomial ideals: quadratic monomial ideals and squarefree monomial ideals with sufficiently many variables relative to the Krull dimension. It is also shown that tensor products, as well as Stanley-Reisner ideals of certain unions, satisfy the multiplicity conjecture if all the components...