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By Sergey Kitaev

There has been a lot curiosity lately within the topic of styles in diversifications and phrases, a brand new department of combinatorics with its roots within the works of Rotem, Rogers and Knuth. This entire reference quantity collects the most ends up in the field.

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332 eight. three. 2 Packing units of styles . . . . . . . . . . . . . . . . . . . . . 335 eight. three. three Packing styles in phrases . . . . . . . . . . . . . . . . . . . . 336 a number of techniques to check styles . . . . . . . . . . . . . . . . . . 339 eight. four. 1 move matrices . . . . . . . . . . . . . . . . . . . . . . . . . 339 eight. four. 2 producing bushes . . . . . . . . . . . . . . . . . . . . . . . . . 339 eight. four. three ECO procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 eight. four. four The insertion encoding . . . . . . . . . . . . . . . . . . . . . . 341 eight. four. five Block decompositions . . . . . . . . . . . . . . . . . . . . . . . 342 A bridge to combinatorics on phrases . . . . . . . . . . . . . . . . . . . 343 eight. five. 1 Morphisms and square-free phrases . . . . . . . . . . . . . . . . 344 eight. five. 2 styles in combinatorics on phrases . . . . . . . . . . . . . . . 345 eight. five. three Powers and sesquipowers . . . . . . . . . . . . . . . . . . . . . 346 eight. five. four Avoidability on a set alphabet . . . . . . . . . . . . . . . . . 347 eight. five. five the most important and maximal phrases for units of prohibitions . . . . . . 348 eight. five. 6 Square-free diversifications . . . . . . . . . . . . . . . . . . . . . 350 eight. 6 common cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 eight. 7 Simsun variations . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 eight. eight An involution on Catalan items . . . . . . . . . . . . . . . . . . . . 357 eight. nine Permutation avoidance video games . . . . . . . . . . . . . . . . . . . . . . 358 Contents xxi nine Extending examine on styles in variations and phrases to different domain names nine. 1 361 Refining patterns/statistics . . . . . . . . . . . . . . . . . . . . . . . . 361 nine. 1. 1 extra on descents and ascents relative to equivalence sessions mod ok . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 nine. 1. 2 k-descents and k-excedences in variations . . . . . . . . . . 365 nine. 1. three Descent pairs with prescribed tops and bottoms . . . . . . . . 365 nine. 2 Place-difference-value styles . . . . . . . . . . . . . . . . . . . . . . 367 nine. three Pattern-avoidance in multisets . . . . . . . . . . . . . . . . . . . . . . 369 nine. four styles in finite approximations of sequences . . . . . . . . . . . . . 370 nine. four. 1 The Peano curve . . . . . . . . . . . . . . . . . . . . . . . . . 370 nine. four. 2 The Dragon curve series and the σ-sequence . . . . . . . . 371 nine. four. three basic learn concerning phrases generated by means of morphisms and styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 nine. five Pattern-avoidance on partial diversifications . . . . . . . . . . . . . . . 375 nine. 6 Signed and coloured diversifications and styles . . . . . . . . . . . . . 377 nine. 7 Generalized issue order . . . . . . . . . . . . . . . . . . . . . . . . . 381 nine. eight Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 nine. eight. 1 Pattern-avoiding set walls . . . . . . . . . . . . . . . . . . 383 nine. eight. 2 Pattern-avoidance in matrices . . . . . . . . . . . . . . . . . . 383 nine. eight. three Pattern-avoidance in n-dimensional gadgets . . . . . . . . . . . 383 nine. eight. four Cyclically closed trend sessions of diversifications . . . . . . . . 384 nine. eight. five Pattern-matching within the cycle constitution of diversifications . . . 384 nine. eight. 6 Equivalence sessions of variations fending off a trend . . . . 385 nine. eight. 7 prolonged pattern-avoidance . . . . . . . . . . . . . . . . . . . 385 an invaluable notions and evidence 387 A. 1 data on diversifications and phrases . . . . . . . . . . . . . . . . . . 387 A. 2 Numbers and lattice paths of curiosity . . . . . . . . . . . . . . . . . . 389 A. 2. 1 Numbers concerned . . . . . . . . . . . . . . . . . . . . . . . . . 390 A. 2. 2 Lattice paths concerned . . . . . . . . . . . . . . . . . . . . . . 396 xxii Contents A. three Pattern-avoiding variations . . . . . . . . . . . . . . . . . . . .

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