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Properties and Applications of a Class of Polynomials

✍ Scribed by S.D. Bedrosian

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
373 KB
Volume
296
Category
Article
ISSN
0016-0032

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✦ Synopsis

A study of c+z.&&x away8 have led ua to examina t?~ Fibonach po&nomid and a tree enumeration polynomial F,,(x) and T"(m), r@vdy. T,,(m) b for lirmw iterative celhhr arrays of n Zeus with a wmmon edge !x+?we~ ao&ctmt m-cyck dia. The we&&mta of T,,(m) huve the 8ame absolude vaha 08 tha8e of F, (x) but alterndw aigw. Ths zeros of the._ve monk polyrwmida are down to be rtd with -2 6 mi < 2, and imagilaaay with x1 d I.2 I. The number of spanmhg trees or %oqv~' of the c&&w @ways ia aho shmm to be given by a generakahn of &dbek'e exp@&cm for the we of m = 4, n = 0, 1, 2, . . . .

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✍ Abram Kagan; Vijay Rohatgi πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 248 KB

A class of polynomials generalizing the polynomial score for a location parameter and possessing a certain invariance property is studied. It is shown that the reciprocal of tile variance of such polynomials is super-additive, a result similar to Stain's inequality. ~ 1997 Elsevier Science B.V.