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 matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible hvectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question. We also prove the 1-dimensional case of a conjecture of Stanley that all matroid h-vectors are pure O-sequences. Finally, we completely characterize...

Perlman, M., and Reisner, S. H. (1973). Archives of Disease in Childhood, 48, 627. Asymmetric crying facies and congenital anomalies. The frequency of hypoplasia of the depressor anguli oris muscle in a newborn population was 41 in 6360 (1 in 155). No adverse factors were noted in the obstetric background of affected infants and the pathogenesis of the lesion is not clear. The incidence of asso...

Abstract Let R(X) = Q[x1,x2 xn] be the ring of polynomials in the variables X = {x1, X2,..., xn} and R*(X) denote the quotient of R(X) by the ideal generated by the elementary symmetric functions. Given a a e Sn, we let g a ( X ) = Yai>ai+1 (xa1,xa2 ... xai). In the late 1970s I. Cessel conjectured that these monomials, called the descent monomials, are a basis for R*(X). Actually, this result ...

A squarefree monomial ideal is called an $f$-ideal if its Stanley–Reisner and facet simplicial complexes have the same $f$-vector. We show that $f$-ideals generated in a fixed degree asymptotic density zero when number of variables goes to infinity. also provide novel algorithms construct small degrees.

Let ∆ be a simplicial complex and χ be an s-coloring of ∆. Biermann and Van Tuyl have introduced the simplicial complex ∆χ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of ∆χ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of ∆χ over a field is set-theoretic complete interse...