Results 1  10
of
294
ALTERNATIVE POLARIZATIONS OF BOREL FIXED IDEALS, ELIAHOUKERVAIRE TYPE RESOLUTION AND DISCRETE MORSE THEORY
"... ar ..."
Combinatorial Commutative Algebra
, 2004
"... The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geo ..."
Abstract

Cited by 125 (5 self)
 Add to MetaCart
The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geometry, graph theory, integer programming, symbolic computation, and statistics. The purpose of this volume is to provide a selfcontained introduction to some of the resulting combinatorial techniques for dealing with polynomial rings, semigroup rings, and determinantal rings. Our exposition mainly concerns combinatorially defined ideals and their quotients, with a focus on numerical invariants and resolutions, especially under gradings more refined than the standard integer grading. This project started at the COCOA summer school in Torino, Italy, in June 1999. The eight lectures on monomial ideals given there by Bernd Sturmfels were later written up by Ezra Miller and David Perkinson and published in [MP01]. We felt it would be nice to add more material and
Resolutions by mapping cones
 Homology Homotopy Appl
"... Many wellknown free resolutions arise as iterated mapping cones. Prominent examples are the EliahouKervaire resolution of stable monomial ideals (as noted by Evans and Charalambous [10]), and the Taylor resolution. The idea of the iterated mapping cone construction is the following: Let I ⊂ R be a ..."
Abstract

Cited by 32 (4 self)
 Add to MetaCart
Many wellknown free resolutions arise as iterated mapping cones. Prominent examples are the EliahouKervaire resolution of stable monomial ideals (as noted by Evans and Charalambous [10]), and the Taylor resolution. The idea of the iterated mapping cone construction is the following: Let I ⊂ R
Hadamard matrices, sequences, and block designs
 SONS, WILEYINTERSCIENCE SERIES IN DISCRETE MATHEMATICS AND OPTIMIZATION
, 1992
"... One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X = (Xij), satisfied the equality of the following inequality, detX2 ≤ ∏ ∑ xij2, and so had maximal dete ..."
Abstract

Cited by 111 (36 self)
 Add to MetaCart
One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X = (Xij), satisfied the equality of the following inequality, detX2 ≤ ∏ ∑ xij2, and so had maximal determinant among matrices with entries ±1. Hadamard actually asked the question of finding the maximal determinant of matrices with entries on the unit disc, but his name has become associated with the question concerning real matrices.
Graded Betti numbers of ideals with linear quotients
 Le Mathematiche LXIII (2008
"... Abstract. In this paper we show that every ideal with linear quotients is componentwise linear. We also generalize the EliahouKervaire formula for graded Betti numbers of stable ideals to homogeneous ideals with linear quotients. 1. ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Abstract. In this paper we show that every ideal with linear quotients is componentwise linear. We also generalize the EliahouKervaire formula for graded Betti numbers of stable ideals to homogeneous ideals with linear quotients. 1.
Integral closure of ideals, rings, and modules
 LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES 336
, 2006
"... ..."
Upper bounds for the Betti numbers of a given Hilbert function
 Comm. Algebra
, 1993
"... Let R: = k[X1,..., XN] be the polynomial ring in N indeterminates over a field k of characteristic 0 with deg(Xi) = 1 for i = 1,..., N, and let I be a homogeneous ideal of R. The Hilbert function of I is the function from N to N which associates to every natural number d the dimension of Id as a k ..."
Abstract

Cited by 80 (0 self)
 Add to MetaCart
Let R: = k[X1,..., XN] be the polynomial ring in N indeterminates over a field k of characteristic 0 with deg(Xi) = 1 for i = 1,..., N, and let I be a homogeneous ideal of R. The Hilbert function of I is the function from N to N which associates to every natural number d the dimension of Id as a kvectorspace. I has an essentially unique minimal graded free resolution
Reformulating the map color theorem
, 2005
"... This paper discusses reformulations of the problem of coloring plane maps with four colors. We include discussion of the Eliahou–Kryuchkov conjecture, the Penrose formula, the vector crossproduct formulation and the reformulations in terms of formations and factorizations due to G. SpencerBrown. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper discusses reformulations of the problem of coloring plane maps with four colors. We include discussion of the Eliahou–Kryuchkov conjecture, the Penrose formula, the vector crossproduct formulation and the reformulations in terms of formations and factorizations due to G. SpencerBrown.
The minimal free resolution of a Borel ideal
"... This paper focuses on the EliahouKervaire minimal free resolution of a Borel ideal. Throughout, S = k[x1,..., xn] is a polynomial ring over a field k. We grade S by deg(xi) = 1 for each i. Let M be an ideal in S. A free resolution of S/M is an exact sequence of homomorphisms of free modules di d1 ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
This paper focuses on the EliahouKervaire minimal free resolution of a Borel ideal. Throughout, S = k[x1,..., xn] is a polynomial ring over a field k. We grade S by deg(xi) = 1 for each i. Let M be an ideal in S. A free resolution of S/M is an exact sequence of homomorphisms of free modules di d1
Results 1  10
of
294