Combinatorial identities for binary necklaces from exact ray-splitting trace formulas
نویسندگان
چکیده
منابع مشابه
Combinatorial identities for binary necklaces from exact ray-splitting trace formulae
Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (Pólya necklaces). 02.10.Eb, 02.30.Lt, 05.45.+b Typeset using REVTEX 1
متن کامل0 10 70 26 v 1 2 6 Ju l 2 00 1 Combinatorial identities for binary necklaces from exact ray - splitting trace formulae
Based on an exact trace formula for a one-dimensional ray-splitting system, we derive novel combinatorial identities for cyclic binary sequences (Pólya necklaces).
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The well-known “splitting necklace theorem” of Alon [1] says that each necklace with k · ai beads of color i = 1, . . . , n can be fairly divided between k “thieves” by at most n(k − 1) cuts. Alon deduced this result from the fact that such a division is possible also in the case of a continuous necklace [0, 1] where beads of given color are interpreted as measurable sets Ai ⊂ [0, 1] (or more g...
متن کاملExact trace formulae for a class of one-dimensional ray-splitting systems
Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman et al. (Phys. Rev. A 46, 6193 (1992)) is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested. PACS: 05.45.+b,03.65.Sq,72.15.Rn
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2001
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1413226