Titlebook: Combinatorics and Commutative Algebra; Richard P. Stanley Textbook 1996Latest edition Birkhäuser Boston 1996 Combinatorics.cls.commutative

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https://doi.org/10.1007/978-981-16-5997-3Let Δ be a finite simplicial complex on the vertex set . = {.,..., .}. Recall that this means that Δ is a collection of subsets of . such that .. The elements of Δ are called .. If . ∈ Δ, then define dim .: = |.| − 1 and dim Δ: = max.(dim .. Let . = dim Δ + 1. Given any field . we now define the . (or .) .[Δ] of the complex Δ.

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Realizing End-to-End Supply Chain Finance,In this chapter we will briefly survey some additional topics related to combinatorics and commutative algebra, mostly dealing with the face ring of a simplicial complex. Our main focus will be on properties of face rings which have applications to combinatorics.

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The Face Ring of a Simplicial Complex,Let Δ be a finite simplicial complex on the vertex set . = {.,..., .}. Recall that this means that Δ is a collection of subsets of . such that .. The elements of Δ are called .. If . ∈ Δ, then define dim .: = |.| − 1 and dim Δ: = max.(dim .. Let . = dim Δ + 1. Given any field . we now define the . (or .) .[Δ] of the complex Δ.

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Further Aspects of Face Rings,In this chapter we will briefly survey some additional topics related to combinatorics and commutative algebra, mostly dealing with the face ring of a simplicial complex. Our main focus will be on properties of face rings which have applications to combinatorics.

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Realizing End-to-End Supply Chain Finance,the text. In general the reader may prefer to begin with Chapter 1 and refer back to this chapter only when necessary. We assume the reader is familiar with standard (first-year graduate) material but has no specialized knowledge of combinatorics, commutative algebra, homological algebra, or algebra

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Combinatorics and Commutative Algebra978-0-8176-4433-8Series ISSN 0743-1643 Series E-ISSN 2296-505X

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Realizing End-to-End Supply Chain Finance,the text. In general the reader may prefer to begin with Chapter 1 and refer back to this chapter only when necessary. We assume the reader is familiar with standard (first-year graduate) material but has no specialized knowledge of combinatorics, commutative algebra, homological algebra, or algebraic topology.