Maximal exponents of polyhedral cones (III)

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題名:	Maximal exponents of polyhedral cones (III)
作者:	Raphael Loewy;Micha A. Perles;Tam, Bit-Shun
貢獻者:	淡江大學數學學系
日期:	2013-07-01
上傳時間:	2013-05-29 14:42:04 (UTC+8)
出版者:	Providence: American Mathematical Society (AMS)
摘要:	Let K be a proper (i.e., closed, pointed, full, convex) cone in Rn. An n × n matrix A is said to be K-primitive if AK ⊆ K and there exists a positive integer k such that Ak(K \ {0}) ⊆ intK; the least such k is referred to as the exponent of A and is denoted by γ(A). For a polyhedral cone K, the maximum value of γ(A), taken over all K-primitive matrices A, is denoted by γ(K). It is proved that for any positive integers m, n, 3 ≤ n ≤ m, the maximum value of γ(K), as K runs through all n-dimensional polyhedral cones with m extreme rays, equals (n−1)(m−1)+1/2(1+(−1)(n−1)m). For the 3-dimensional case, the cones K and the corresponding K-primitive matrices A such that γ(K) and γ(A) attain the maximum value are identified up to respectively linear isomorphism and cone-equivalence modulo positive scalar multiplication.
關聯:	Transactions of the American Mathematical Society 365(7), pp.3535-3573
DOI:	10.1090/S0002-9947-2013-05879-5
顯示於類別:	[數學學系暨研究所] 期刊論文

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