Monomial regular sequences

Mermin, Jeffrey

doi:10.1090/s0002-9939-10-10244-5

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Introduction2

Background and Notation1

Macaulay's Theorem1

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2016

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Cited by 9 publications

(6 citation statements)

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“…We conclude that the EGH conjecture is true when I is a monomial ideal. A related result was proved in [3] when I is generated by monomials of degree 2 and in [6] when f 1 , . .…”

Section: Introductionmentioning

confidence: 82%

Hilbert functions of monomial ideals containing a regular sequence

Abedelfatah

2016

Isr. J. Math.

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Let M be an ideal in K[x 1 , . . . , xn] (K is a field) generated by products of linear forms and containing a homogeneous regular sequence of some length. We prove that ideals containing M satisfy the Eisenbud-Green-Harris conjecture and moreover prove that the Cohen-Macaulay property is preserved. We conclude that monomial ideals satisfy this conjecture. We obtain that h-vector of Cohen-Macaulay simplicial complex ∆ is the h-vector of Cohen-Macaulay (a 1 − 1, . . . , at − 1)-balanced simplicial complex where t is the height of the Stanley-Reisner ideal of ∆ and (a 1 , . . . , at) is the type of some regular sequence contained in this ideal.

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“…We conclude that the EGH conjecture is true when I is a monomial ideal. A related result was proved in [3] when I is generated by monomials of degree 2 and in [6] when f 1 , . .…”

Section: Introductionmentioning

confidence: 82%

Hilbert functions of monomial ideals containing a regular sequence

Abedelfatah

2016

Isr. J. Math.

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“…Compression and compressed ideals have been used by Macaulay and others [CL,Ma,Me1,Me2,MP1,MP2,MPS,MH] to study Hilbert functions and Betti numbers. In [Me2], Mermin proves the following: Theorem 2.13 ([Me2]).…”

Section: Background and Notationmentioning

confidence: 99%

The Lex-Plus-Powers Conjecture holds for pure powers

Mermin

Murai

2011

Advances in Mathematics

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“…Macaulay's theorem is known to hold in many quotients of R; see [4,11,12,[14][15][16]22]. The first extension was given by Kruskal [12] and Katona [11], who showed that it holds in S = R/(x 2 1 , .…”

Section: Macaulay's Theoremmentioning

confidence: 99%