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| Sagan B.E. — The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions |
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| Предметный указатель |
Module, irreducible 12
Module, isomorphism 19
Module, permutation module MA 56
Module, reducible 12
Module, Specht 62
Module, tensor product 44
Module, unimodal sequence 209
Moebius, function 219
Moebius, inversion 206 219
Moebius, inversion theorem 220
Monomial symmetric function 151
Multiplicative 154
Murnaghan — Nakayama rule 180
n-chain 58 192
Natural labeling 150
Neighbors 213
Normal diagram 112
North 129
North, step 129 158
Novelli — Pak — Stoyanovskii algorithm 125—132
Orbit 48 210
Order, dominance see “Dominance order”
Order, lexicographic 59
Order, preserving 197
Orthogonal complement 15
Outer corner 76
P-equivalence 99
P-tableau 93
Partial order 58
Partial permutation 101
Partial tableau 92
Partially ordered set see “Poset”
Partition 2
Partition, boundary 117
Partition, dominance, lemma 59
Partition, dominance, order 58
Partition, hook 124
Partition, hooklength 124
Partition, length 152
Partition, normal 112
Partition, set 215
Partition, skew 112
Partition, strict 139
Path, Gessel — Viennot 158
Path, Hillman — Grassl 148
Path, insertion 92
Path, Novelli — Pak — Stoyanovskii 127
Path, reverse Hillman — Grassl 149
Path, reverse Novelli — Pak — Stoyanovskii 128
Permutation 1
Permutation matrix 6
Permutation, adjacent transposition 4
Permutation, cycle see “Cycle”
Permutation, fixedpoint 2
Permutation, generalized 169
Permutation, involution 2
Permutation, lattice 176
Permutation, matrix 6
Permutation, module  56
Permutation, one-line notation 2
Permutation, partial 101
Permutation, representation 8
Permutation, reversal 97
Permutation, shadow diagram 108
Permutation, shadow line 107
Permutation, skeleton of 110
Permutation, transposition 4
Permutation, transposition, adjacent 4
Permutation, two-line notation 1
placement 93
Polytabloid 61
POSET 58
Poset, ample 209
Poset, ascending chain 194
Poset, automorphism 204
Poset, Boolean algebra 58 192
Poset, chain 194
Poset, covering relation 58
Poset, descending chain 194
Poset, differential 196
Poset, down operator 196
Poset, down operator, Fibonacci 218
Poset, down operator, r-differential 218
Poset, down operator, up operator 196
Poset, graded 195
Poset, greatest lower bound 192
Poset, growth 197
Poset, Hasse diagram 58
Poset, incomparable elements 58
Poset, interval 219
Poset, isomorphism 220
Poset, join 192
Poset, lattice 192
Poset, least upper bound 192
Poset, locally finite 219
Poset, lower order ideal 85
Poset, maximal element 69
Poset, maximum element 69
Poset, meet 192
Poset, minimal element 69
Poset, minimum element 69
Poset, n-chain 58 192
Poset, natural labeling 150
Poset, order preserving 197
Poset, product 197
Poset, r-differential 218
Poset, rank 195
Poset, rank-selected 204
Poset, refinement of 59
Poset, reverse partition 150
Poset, saturated chain 194
Poset, symmetric 208
Poset, unimodal 208
Power sum symmetric functions 152 154
Principle of inclusion-exclusion 206 219
Product of characters 168
Product of posets 197
Proper coloring 213
Q-equivalence 111
Q-tableau 93
r-differential poset 218
Rank 195
Rank-selected poset 204
Reciprocity law of Frobenius 48
Recording tableau 93
Reducibility 12
Reducibility, complete 17
refinement 59
Representation 4
Representation of cyclic groups 5
Representation, completely reducible 17
Representation, coset 9 20
Representation, defining 5 8 11 14 18 20
Representation, degree 4
Representation, direct sum 13
Representation, induced 45
Representation, irreducible 12
Representation, matrix 4
Representation, permutation 8
Representation, reducible 12
Representation, regular 8 11
Representation, restricted 45
Representation, sign 5 11 19
Representation, tensor product 43
Representation, trivial 4 11 18
Representation, Young’s natural 74
Restricted representation 45
Reversal 97
Reverse ballot sequence or lattice permutation 176
Reverse path, code 129
| Reverse path, Hillman — Grassl 149
Reverse path, Novelli — Pak — Stoyanovskii 128
Reverse plane partition 147
Rim hook 180
Rim hook, tableau 184
Robinson — Schensted algorithm 92—94
Roby, T.W. 197
Rooted tree 138
Rooted tree, hook 138
Rooted tree, hooklength 138
Row word 101
Row-stabilizer 60
Rule, branching 77
Rule, Littlewood — Richardson 177 183
Rule, local 199
Rule, Murnaghan — Nakayama 180
Rule, Young 85 174
Saturated 194
Schuetzenberger, M.-P. 106 112 121 173 177
Schur function 155
Schur function, skew 175
Schur’s lemma for matrices 22
Schur’s lemma for modules 22
Schur’s lemma, over complex field 23
Semistandard, basis 82
Semistandard, Young tableau 81
Sequence, symmetric 208
Sequence, unimodal 208
Set partition 215
Set partition, block 215
Set partition, independent 215
Set partition, stable 215
Set partition, type 215
Shadow 107
Shadow, diagram 108
Shadow, line 107
Shadow, line, x-coordinate 108
Shadow, line, y-coordinate 108
SHAPE 54
Shape, rooted tree 138
Shape, shifted 139
Shape, skew 112
Shifted, hook 139
Shifted, hooklength 139
Shifted, shape 139
Sign lemma 64
Sign of a permutation 4
Sign of a rim hook tableau 185
Sign of lattice paths 160
Sign, representation 5 11 19
Skeleton 110
Skew, diagram 112
Skew, hook 180
Skew-symmetric functions 163
Slide 113
Slide, modified backward 128
Slide, modified forward 126
Slide, sequence 114
South 129
Specht module 62
Stable, partition 215
Stable, set 215
Standard, basis 67
Standard, Young tableau 66
Stanley, R.P. 150 195—197 214
Step, eastward 158
Step, northward 129 158
Step, westward 129
Straightening algorithm 70
Strict partition 139
Submodule 10
Submodule, theorem 65
Subsequence 97
Subsequence, decreasing 97
Subsequence, increasing 97
Subsequence, k-decreasing 103
Subsequence, k-increasing 103
Subsequence, length 98
Superstandard tableau 157
Symmetric function, chromatic 214
Symmetric function, complete homogeneous 152
Symmetric function, elementary 152 154
Symmetric function, grading 152
Symmetric function, monomial 151
Symmetric function, multiplicative 154
Symmetric function, power sum 152 154
Symmetric function, ring of 151
Symmetric function, Schur 155
Symmetric function, Schur, skew 175
Symmetric, group 1
Symmetric, poset 208
Symmetric, sequence 208
Tableau 55
Tableau of shape  55
Tableau, antidiagonal strip 113
Tableau, column-stabilizer 60
Tableau, content 78
Tableau, delta operator 121
Tableau, descent 206
Tableau, dominance, lemma 82
Tableau, dominance, order 82
Tableau, dual equivalence 117
Tableau, equivalent 114
Tableau, evacuation 122
Tableau, Garnir element 71
Tableau, generalized 78
Tableau, hook 126
Tableau, insertion tableau 93
Tableau, miniature 118
Tableau, P-tableau 93
Tableau, partial 92
Tableau, Q-tableau 93
Tableau, recording tableau 93
Tableau, rim hook 184
Tableau, row descent 70
Tableau, row equivalent 55
Tableau, row word 101
Tableau, row-stabilizer 60
Tableau, semistandard 81
Tableau, standard 66
Tableau, superstandard 157
Tableau, type 78
Tableau, union 120
Tabloid 55
Tabloid of shape 55
Tabloid, column 72
Tabloid, dominance, lemma 68
Tabloid, dominance, order 68
Tensor product of matrices 25
Tensor product of representations 43
Tensor product of vector spaces 26
Theorem, Maschke, for matrices 17
Theorem, Maschke, for modules 16
Theorem, Moebius inversion 220
Theorem, submodule 65
Thomas, G.P. 177
Total order 58
Totally ordered set 58
Transposition 4
Transposition, adjacent 4
TREE 217
Type, cycle 2
Type, set partition 215
Type, tableau 78
Unimodal, module sequence 209
Unimodal, poset 208
Unimodal, sequence 208
Union of tableaux 120
Up operator in a differential poset 196
Up operator in Young’s lattice 193
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