Quasi-symmetric functions and the Chow ring of the stack of expanded pairs

Oesinghaus, Jakob

doi:10.48550/arxiv.1806.10700

Cited by 3 publications

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“…defined by forgetting the last m marked points. Images of M g,n+m give a good filtration on M g,n in the sense of [21,Definition 5]. Suppose we have a finite degree operational Chow class on M g,n which pulls back to a tautological relation on M g,n+m for sufficiently large m. Then we can try to prove that the relation holds in M g,n .…”

Section: X-valued Tautological Ringmentioning

confidence: 99%

Tautological relations for stable maps to a target variety

Bae

2020

Arkiv För Matematik

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Section: X-valued Tautological Ringmentioning

confidence: 99%

Tautological relations for stable maps to a target variety

Bae

2020

Arkiv För Matematik

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“…Originally introduced by Gessel in 1984 [Gessel84], it has since found applications (e.g.) to enumerative combinatorics ([Sagan20, Chapter 8], [Stanle24,], [GesZhu18]), multizeta values (e.g., [Hoffma15]), algebraic geometry ( [Oesing18]) and the representation theory of 0-Hecke algebras ([Meliot17, §6.2]).…”

Section: Introductionmentioning

confidence: 99%

Dual Creation Operators and a Dendriform Algebra Structure on the Quasisymmetric Functions

Grinberg¹

2017

Can. j. math.

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Abstract.e dual immaculate functions are a basis of the ring QSym of quasisymmetric functions, and form one of the most natural analogues of the Schur functions.e dual immaculate function corresponding to a composition is a weighted generating function for immaculate tableaux in the same way as a Schur function is for semistandard Young tableaux; an "immaculate tableau" is de ned similarly to a semistandard Young tableau, but the shape is a composition rather than a partition, and only the rst column is required to strictly increase (whereas the other columns can be arbitrary; but each row has to weakly increase). Dual immaculate functions have been introduced by Berg, Bergeron, Saliola, Serrano and Zabrocki in arXiv:. , and have since been found to possess numerous nontrivial properties.In this note, we prove a conjecture of Mike Zabrocki which provides an alternative construction for the dual immaculate functions in terms of certain "vertex operators". e proof uses a dendriform structure on the ring QSym; we discuss the relation of this structure to known dendriform structures on the combinatorial Hopf algebras FQSym and WQSym.

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“…This interpretation was used in [BR08] to give cohomological proofs of various properties of QSym; however, it seems that much more could be done from this perspective. A recent construction, which appears closely related, identifes QSym with the Chow ring of an algebraic stack of expanded pairs [Oes18].…”

mentioning

confidence: 99%

Asymmetric function theory

Pechenik,

Searles

2019

Preprint

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The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.

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Quasi-symmetric functions and the Chow ring of the stack of expanded pairs

Cited by 3 publications

References 0 publications

Tautological relations for stable maps to a target variety

Tautological relations for stable maps to a target variety

Dual Creation Operators and a Dendriform Algebra Structure on the Quasisymmetric Functions

Asymmetric function theory

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