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| Sagan B.E. — The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions |
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| Предметный указатель |
action 7
Action on generalized tableaux 79
Action on standard tableaux 55
Action on tabloids 55
Action, orbit 48 210
Action, trivial 11
Adjacent transposition 4
Algebra 4
Algebra, boolean 58 192
Algebra, center of 27
Algebra, commutant 23
Algebra, endomorphism 23
Algebra, full matrix 4
Algebra, group 8
Algebra, Weyl 197
Algorithm, backward slide 113
Algorithm, deletion 94
Algorithm, delta operator 121
Algorithm, dual Knuth 172
Algorithm, evacuation 122
Algorithm, forward slide 113
Algorithm, Greene — Nijenhuis — Wilf 137
Algorithm, Hillman — Grassl 148—150
Algorithm, insertion 92
Algorithm, Knuth 169—171
Algorithm, modified slide 126—128
Algorithm, Novelli — Pak — Stoyanovskii 125—132
Algorithm, Robinson — Schensted 92—94
Algorithm, straightening 70
Alternant 164
ample 209
Antidiagonal strip 113
Appel — Haken 213
Arm length of a hook 125
Arm of a hook 125
Automorphism 204
Backward slide 113
Backward slide, modified 128
Ballot sequence 176
Block 215
Boolean algebra 58 192
Boundary of a partition 117
Branching rule 77
Candidate cell 128
Cauchy identity 171
cell 54
Cell, candidate 128
Center 27
Center of commutant algebra 27 29
Center of endomorphism algebra 30
Center of matrix algebra 27
centralizer 3
Chain, ascending 194
Chain, descending 194
Chain, saturated 194
CHARACTER 30
Character, defining 31
Character, inner product 34
Character, linear 31
Character, orthogonality relations 35
Character, orthogonality relations, first kind 35
Character, orthogonality relations, second kind 42
Character, product 168
Character, regular 31
Character, table 32
Characteristic map 167 168
Chromatic, polynomial 214
Chromatic, symmetric function 214
Class function 32
Code 129
Coloring 213
Coloring, proper 213
Column insertion 95
Column tabloid 72
Column-stabilizer 60
Commutant algebra 23
Complement 13
Complement, orthogonal 15
Complete homogeneous symmetric functions 152 154
Complete reducibility 17
components 216
composition 67
Conjugacy of group elements 3
Conjugacy, class 3
Content 78
Converge 144
Corner 76
Cover 58
CYCLE 2
Cycle in a graph 217
Cycle of length k 2
Cycle, type 2
Cyclic module 57
Decreasing subsequence 97
Degree of a monomial 151
Degree of a power series 144
Degree of a representation 4
Deletion 94
Delta operator 121
Descent, permutation 221
Descent, row 70
Descent, tableau 206
Determinantal formula 132
Differential poset see “Poset differential”
Dihedral group 51
Direct sum 13
Dominance lemma for partitions 59
Dominance lemma for tableaux 82
Dominance lemma for tabloids 68
Dominance order for partitions 58
Dominance order for tableaux 82
Dominance order for tabloids 68
Down operator in a differential poset 196
Down operator in Young’s lattice 193
Dual Cauchy identity 172
Dual equivalence of tableau 117
Dual Knuth equivalence 111
Dual Knuth equivalence of tableaux 113
Dual Knuth relations 111
East 129
Elementary symmetric functions 152 154
Endomorphism algebra 23
EQUIVALENCE 99
Equivalence, dual Knuth 111
Equivalence, dual Knuth, of tableaux 113
Equivalence, dual tableau 117
Equivalence, Knuth 100
Equivalence, Knuth, of tableaux 113
Equivalence, P 99
Equivalence, Q 111
Equivalence, tableaux 114
Equivalent, column tableaux 72
Equivalent, modules 19
Equivalent, row tableaux 55
Euler, L. 144 145
Evacuation 122
Ferrers diagram 54
Fibonacci, number 218
Fibonacci, poset 218
FixedPoint 2
Fomin, S. 195 197
Formal power series 142
Formal power series, convergence of 144
Formal power series, degree 144
Formal power series, homogeneous of degree n 151
Forward slide 113
Forward slide, modified 126
Four color theorem 214
Frame — Robinson — Thrall formula 124
Frobenius reciprocity law 48
| Frobenius — Young formula 132
Frobenius, G. 45 166
Full matrix algebra 4
Garnir element of a pair of sets 70
Garnir element of a tableau 71
General linear group of a vector space 6
General linear group of matrices 4
Generalized permutation 169
Generalized Young tableau 78
Generating function 142
Generating function, weight 145
Gessel — Viennot 158
Graded 195
Grading 152
Graph 213
Graph, chromatic polynomial 214
Graph, coloring 213
Graph, components 216
Graph, cycle 217
Graph, Four Color Theorem 214
Graph, independent partition 215
Graph, independent set 215
Graph, isomorphism 217
Graph, neighbors 213
Graph, proper coloring 213
Graph, stable partition 215
Graph, stable set 215
Graph, tree 217
Greatest lower bound 192
Greene — Nijenhuis — Wilf algorithm 137
Greene, C. 102 173
Group, action see “Action”
Group, algebra 8
Group, character 30
Group, cyclic 5
Group, dihedral 51
Group, general linear 4 6
Group, symmetric 1
Growth 197
Haiman, M.D. 117
Hasse diagram 58
Hasse diagram, normal 112
Hasse diagram, skew 112
Hillman — Grassl algorithm 148—150
Homogeneous of degree n 151
Homomorphism 18
Homomorphism, corresponding to a tableau 80
Hook 124
Hook, arm 125
Hook, formula 124
Hook, leg 125
Hook, rim or skew 180
Hook, rooted tree 138
Hook, shifted 139
Hook, tableau 126
Hooklength 124
Hooklength, rooted tree 138
Hooklength, shifted 139
Inclusion-exclusion see “Principle of Inclusion-Exclusion”
Incomparable 58
Increasing subsequence 97
Independent, partition 215
Independent, set 215
Induced representation 45
Inequivalent 19
Inner corner 76
Inner product of characters 34
Inner product, invariant 14
Insertion tableau 93
Insertion, column 95
Insertion, path 92
Insertion, row 92
Interval of a poset 219
Invariant, inner product 14
Invariant, subspace 10
Involution 2
Irreducibility 12
Isomorphism, graph 217
Isomorphism, module 19
Isomorphism, poset 220
Jacobi — Trudi determinants 158 182
James, G.D. viii 53 63 66 182
Jeu de taquin 116 173
Jeu de taquin, backward slide 113
Jeu de taquin, forward slide 113
Jeu de taquin, modified backward slide 128
Jeu de taquin, modified forward slide 126
Join 192
k-decreasing subsequence 103
k-increasing subsequence 103
Knuth, D.E., algorithm 169—171
Knuth, D.E., dual algorithm 172
Knuth, D.E., dual equivalence 111
Knuth, D.E., dual equivalence, of tableaux 113
Knuth, D.E., dual relations 111
Knuth, D.E., dual relations, first kind 111
Knuth, D.E., dual relations, second kind 111
Knuth, D.E., equivalence 100
Knuth, D.E., equivalence, of tableaux 113
Knuth, D.E., relations 99 173
Kostka numbers 85
Lattice permutation 176
Lattice, path 158
Lattice, path, involution 161
Lattice, path, labelings 158—159
Lattice, path, sign 160
Lattice, path, weight 159—160
Lattice, poset 192
Lattice, Young 192
Lattice, Young, down operator 193
Lattice, Young, up operator 193
Least upper bound 192
Ledermann, W. vii
Leg length of a hook 125
Leg length of a rim or skew hook 180
Leg of a hook 125
Lemma, dominance see “Dominance lemma”
Lemma, Schur’s 22
Lemma, sign 64
Length 152
Length of a subsequence 98
Lexicographic order 59
Littlewood — Richardson, coefficient 175
Littlewood — Richardson, rule 177 183
Local rules 199
Locally finite 219
Log concave 189
Lower order ideal 85
MacDonald, I.G. viii 164
Maschke’s theorem for matrices 17
Maschke’s theorem for modules 16
Matrix 4
Matrix, direct sum 13
Matrix, tensor product 25
Maximal element 69
Maximum element 69
Meet 192
Miniature tableau 118
Minimal element 69
Minimum element 69
Modified slide 126—128
Module 6
Module, complement 13
Module, cyclic 57
Module, direct sum 13
Module, endomorphism algebra 23
Module, equivalent 19
Module, generated by a vector 57
Module, homomorphism 18
Module, inequivalent 19
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