## American Mathematical Society TranslationsThe articles in this collection present new results in combinatorics, algebra, algebraic geometry, dynamical systems, analysis, and probability. Of particular interest is the survey article by A. N. Kirillov devoted to combinatorics of Young diagrams and related problems of representation theory. Also included are articles devoted to the eightieth birthday of renowned Russian mathematician, V. A. Rokhlin, ``Remembrances of V. A. Rokhlin'', by I. R. Shafarevich, and ``An Unfinished Project of V.A. Rokhlin'', by V. N. Sudakov. The results, ideas, and methods given in the book will be of interest to a broad range of specialists. |

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### Contents

1 | |

Combinatorics of Young Tableaux and Configurations | 17 |

On Integral Models of Affine Toric Varieties | 99 |

Biorthogonal Wavelet Bases with Rational Masks | 147 |

QPseudodifference Universal DrinfeldSokolov Reduction | 169 |

Effective Construction of Local Parameters of Irreducible Components of | 201 |

From the Editorial Board | 233 |

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admissible configuration ahuost algebraic variety algorithm assume asymptotic bijection biorthogonal pair block coefficients coincides combinatorial computation condition configuration of type Consequently Consider partitions construction corresponding defined definition Denote DS-reduction elements embedding English transl equal equation example exists filters finite formula g-binomial Heisenberg highest weight homogeneous polynomials inequality integer introduce irreducible components irreducible representation isomorphic kernel Kostant Kostant partition function Kostka polynomials Kostka-Foulkes polynomials large deviations Lemma Lie algebra linear forms Math Mathematical matrix measurable partitions Mises functionals multiplicity notation obtain operator partition lattice permutation Poisson bracket polyphase matrix prime ideal problem proof of Theorem proved r-matrix Recall rigged configurations right-hand side Rokhlin satisfying Schur functions Section sequence solutions space statistics STY(A subset subspace symmetric tableau tableaux of shape tensor product Theorem 3.1 theory topology unimodality vector wavelet bases Young diagrams Young tableaux zero

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Page 3 - A set is said to be finite if it contains a finite number of elements otherwise, it is infinite. The size of a finite set is the number of elements in it, this is denoted by | S |. 1.2.8 Power Set The set of all subsets of a set 'S' is called the power set of 'S