Inductive Proof of Macaulays Theorem
Inductive Proof of Macaulays Theorem
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In our eReader you can find the full English version of the book. Read Inductive Proof of Macaulays Theorem Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Inductive Proof of Macaulays Theorem
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Then for /c = 1, . . . , n, i:\S, {B)\ > i:\S. (L{n, d, \B\))\ .
i-1 «=1 Proof. The assumption concerning sets of the form C is given for technical reasons, and lemma 8 shows that this assumption is always satisfied. For now though, this assumption allows one to conclude that T{B) is Borel- fixed.
K T{B) is a lexicographic set, then since it contains \B\ power products of degree d, then it is the lexicographic set L{n, d, \B\). The lemma then follows trivially since for each i = 1, . . . , n, \...Si{B)\ = \S, {T{B))\ = \S, {L{n, d, \B\)\ .
Assume otherwise that T{B) is not lexicographic. Let h — x^' • ■ ■ x^" be the lexicographically last power product of T{B), and let g = i/ • • • x^" be the lexicographically first degree d power product not in T{B) — {h}, where a^ and 6„ are non-zero. Since T{B) is not lexicographic g>h, and by lemma 6, u j:\s, {E)\.
What to read after Inductive Proof of Macaulays Theorem?
You can find similar books in the "Read Also" column, or choose other free books by Thomas Dube to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Then for /c = 1, . . . , n, i:\S, {B)\ > i:\S. (L{n, d, \B\))\ .
i-1 «=1 Proof. The assumption concerning sets of the form C is given for technical reasons, and lemma 8 shows that this assumption is always satisfied. For now though, this assumption allows one to conclude that T{B) is Borel- fixed.
K T{B) is a lexicographic set, then since it contains \B\ power products of degree d, then it is the lexicographic set L{n, d, \B\). The lemma then follows trivially since for each i = 1, . . . , n, \...Si{B)\ = \S, {T{B))\ = \S, {L{n, d, \B\)\ .
Assume otherwise that T{B) is not lexicographic. Let h — x^' • ■ ■ x^" be the lexicographically last power product of T{B), and let g = i/ • • • x^" be the lexicographically first degree d power product not in T{B) — {h}, where a^ and 6„ are non-zero. Since T{B) is not lexicographic g>h, and by lemma 6, u j:\s, {E)\.
What to read after Inductive Proof of Macaulays Theorem?
You can find similar books in the "Read Also" column, or choose other free books by Thomas Dube to read onlineMoreLess
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