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- W2952208768 abstract "We study the combinatorics of addition using balanced digits, deriving an analog of Holte's amazing for carries in usual addition. The eigenvalues of this matrix for base b balanced addition of n numbers are found to be 1,1/b,...,1/b^n, and formulas are given for its left and right eigenvectors. It is shown that the left eigenvectors can be identified with hyperoctahedral Foulkes characters, and that the right eigenvectors can be identified with hyperoctahedral Eulerian idempotents. We also examine the carries that occur when a column of balanced digits is added, showing this process to be determinantal. The transfer matrix method and a serendipitous diagonalization are used to study this determinantal process." @default.
- W2952208768 created "2019-06-27" @default.
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- W2952208768 date "2013-09-19" @default.
- W2952208768 modified "2023-09-27" @default.
- W2952208768 title "Combinatorics of balanced carries" @default.
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