In this paper we introduce p−Ferrer diagram, note that 1− Ferrer diagram are the usual Ferrer diagrams or Ferrer board, and corresponds to planar partitions. To any p−Ferrer diagram we associate a p−Ferrer ideal. We prove that p−Ferrer ideal have Castelnuovo mumford regularity p + 1. We also study Betti numbers , minimal resolutions of p−Ferrer ideals. Every p−Ferrer ideal is p−joined ideals in...

Theoretical foundations of a new algorithm for determining the p-capitulation type K ( )  of a number field K with p-class rank = 2  are presented. Since K ( )  alone is insufficient for identifying the second p-class group p K K = 2 Gal(F | ) G of K, complementary techniques are developed for finding the nilpotency class and coclass of G . An implementation of the complete algorithm in the ...

Nowadays, XML is becoming the standard for electronic information representation and exchange in our lives. Access to information presented in hyperlinked XML documents and other formats have always been in demand by users. In this paper, we describe the architecture, implementation, and evaluation of the P-RANK system built to address the requirement for efficient ranked keyword search over hy...

We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on P5. In characteristic p, we obtain rank two bundles on P4 and rank three bundles on P5. In arbitrary characteristic, we obtain rank three bundles on P4 and rank two bundles on the quadric S5 in P6.

A rank one local system L on a smooth complex algebraic variety M is 1-admissible if the dimension of the first cohomology group H(M,L) can be computed from the cohomology algebra H∗(M, C) in degrees ≤ 2. Under the assumption that M is 1-formal, we show that all local systems, except finitely many, on a non-translated irreducible component W of the first characteristic variety V1(M) are 1-admis...

Abstract Let p be an odd prime and G a finite group with $$O_{p'}(G)=1$$ O p ′ ( G ) = 1 of -rank at most 2 that contains ...

We introduce concepts of intermediate rank for countable groups that “interpolate” between consecutive values of the classical (integer-valued) rank. Various classes of groups are proved to have intermediate rank behaviors. We are especially interested in interpolation between rank 1 and rank 2. For instance, we construct groups “of rank 7 4 ”. Our setting is essentially that of non positively ...