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|a (TOE)ost5653979
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|a (TOE)5653979
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|a TOE
|c TOE
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|a GDWR
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|a 99
|2 edbsc
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|a E 1.99: conf-920662--1
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|a E 1.99:la-ur-92-266
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|a E 1.99: conf-920662--1
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|a conf-920662--1
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|a la-ur-92-266
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|a Induced cycle structures of the hyperoctahedral group
|h [electronic resource]
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| 260 |
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|a Washington, D.C. :
|b United States. Department of Energy ;
|a Oak Ridge, Tenn. :
|b distributed by the Office of Scientific and Technical Information, U.S. Department of Energy,
|c 1992.
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| 300 |
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|a Pages: (16 p) :
|b digital, PDF file.
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| 336 |
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|a text
|b txt
|2 rdacontent.
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| 337 |
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|a computer
|b c
|2 rdamedia.
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| 338 |
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|a online resource
|b cr
|2 rdacarrier.
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| 500 |
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|a Published through SciTech Connect.
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| 500 |
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|a 06/01/1992.
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| 500 |
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|a "la-ur-92-266"
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| 500 |
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|a " conf-920662--1"
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| 500 |
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|a "DE92007570"
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| 500 |
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|a 4. conference on formal power series and algebraic combinatorics, Montreal (Canada), 15-19 Jun 1992.
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| 500 |
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|a Chen, W.Y.C.
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| 520 |
3 |
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|a The hyperoctahedral group B{sub n} is treated as the automorphism group of the n-dimensional hypercube, denoted Q{sub n}, which is nowadays understood to be a graph on 2ⁿ vertices. It is well-known that B{sub n} can be represented by the group of signed permutations. In other words, any signed permutation induces a permutation on the vertices of Q{sub n} which preserves adjacencies. Moreover, signed permutations also a permutation group on the edge of Q{sub n}, denoted H{sub n}. We study the cycle structures of both B{sub n} and H{sub n}. The technique proposed here is to determine the induced cycle structure of a signed permutation by the number of fixed vertices or fixed edges of a signed permutation in the cyclic group generated by a signed permutation of given type. Here we directly define the type of a signed permutation by a double partition based on its signed cycle decomposition. In this way, we obtain explicit formulas for the number of induced cycles on vertices as well as edges of Q{sub n} of a signed permutation in terms of its type. By further exploring the connection between cycle indices and the structure of fixed points, we obtain the cycle indices of both B{sub n} and H{sub n}. Our formula for the cycle index of B{sub n}is much more natural and considerably simpler than that of Harrison and High. Meanwhile, the cycle structure of H{sub n} seems to have been untouched before, although it is well motivated by nonisomorphic edge colorings of Q{sub n} as well as by the recent interest in symmetries of computer networks.
|
| 536 |
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|b W-7405-ENG-36.
|
| 650 |
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7 |
|a Symmetry Groups.
|2 local.
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| 650 |
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7 |
|a Computer Networks.
|2 local.
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| 650 |
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7 |
|a Polynomials.
|2 local.
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| 650 |
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7 |
|a Power Series.
|2 local.
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| 650 |
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7 |
|a Functions.
|2 local.
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| 650 |
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7 |
|a Series Expansion.
|2 local.
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| 650 |
|
7 |
|a General And Miscellaneous//Mathematics, Computing, And Information Science.
|2 edbsc.
|
| 710 |
2 |
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|a Los Alamos National Laboratory.
|4 res.
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| 710 |
1 |
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|a United States.
|b Department of Energy.
|4 spn.
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| 710 |
1 |
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|a United States.
|b Department of Energy.
|b Office of Scientific and Technical Information.
|4 dst.
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| 856 |
4 |
0 |
|u http://www.osti.gov/scitech/biblio/5653979
|z Online Access
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| 907 |
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|a .b5971833x
|b 03-06-23
|c 05-26-10
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| 998 |
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|a web
|b 09-09-16
|c f
|d m
|e p
|f eng
|g
|h 0
|i 3
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| 956 |
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|a Information bridge
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| 999 |
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|i 5276d844-db35-58af-bf0b-54035d581bf3
|s d64f6c3d-4e3e-5f65-ad9f-140330f6b153
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| 952 |
f |
f |
|p Can circulate
|a University of Colorado Boulder
|b Online
|c Online
|d Online
|e E 1.99: conf-920662--1
|h Superintendent of Documents classification
|i web
|n 1
|
