Titlebook: Counting with Symmetric Functions; Anthony Mendes,Jeffrey Remmel Book 2015 Springer International Publishing Switzerland 2015 RSK algorith

Vulnerary

Walther in Geschichte und Forschung,This chapter applies the machinery of ring homomorphisms on symmetric functions to understand consecutive pattern matches in permutations, words, cycles, and in alternating permutations.

陳列

滑稽

來就得意

Symmetric Functions,The ring of symmetric functions is introduced. The six standard bases for symmetric functions; namely, the monomial, elementary, homogeneous, power, forgotten, and Schur symmetric functions, are defined. Numerous relationships between these functions are proved.

Hemiparesis

Counting with the Elementary and Homogeneous Symmetric Functions,The relationship between the elementary and homogeneous symmetric functions, specifically the expansion involving brick tabloids, is used to find an assortment of generating functions. We are able to count and refine permutations according to restricted appearances of descents and prove a variety of results about words.

預(yù)知

Counting with RSK,The RSK algorithm is introduced and used to find generating functions for permutation statistics. Connections are made to increasing subsequences in permutations and words and the Schur symmetric functions. A .-analogue of the hook length formula is proved, and the Hillman-Grassl algorithm is introduced.

進(jìn)入

Counting Problems That Involve Symmetry,Symmetric functions are used to prove Pólya’s enumeration theorem, allowing us to count objects modulo symmetries.

壓倒性勝利

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EPT

https://doi.org/10.1007/978-3-319-23618-6RSK algorithm; bijective proofs; combinatorics; generating functions; symmetric functions