On quasisymmetric power sums

Ballantine, Cristina; Daugherty, Zajj; Hicks, Angela; Mason, Sarah; Niese, Elizabeth

doi:10.1016/j.jcta.2020.105273

Cited by 9 publications

(11 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 4.2. The bases of type 1 quasisymmetric power sums {Ψ α } α n≥0 and type 2 quasisymmetric power sums {Φ α } α n≥0 , introduced by Ballantine, Daugherty, Hicks, Mason and Niese [3] as the scaled duals of the noncommutative power sums of the first and second kind [7], were shown in the same paper to satisfy all of properties (1) to (6).…”

Section: Quasisymmetric and Noncommutative Power Sumsmentioning

confidence: 98%

“…By an upper-triangularity argument against the monomial basis, {p α } α n≥0 is a basis for QSym. Note that the basis {p α } α n≥0 is distinct from the bases {Ψ α } α n≥0 and {Φ α } α n≥0 of quasisymmetric power sums introduced in [3], since although they expand into the monomial basis with nonnegative coefficients, those coefficients are not always integer.…”

Section: The Basis Of Combinatorial Power Sumsmentioning

confidence: 99%

“…Quasisymmetric analogues of classical symmetric function bases facilitate the translation between the language of symmetric functions and the language of quasisymmetric functions, and have been discovered for monomial symmetric functions [8], Schur functions [4,11] and, most recently, for power sum symmetric functions [3]. Power sum symmetric functions are of especial interest because they encode the class values of the characters of the symmetric group under the Frobenius characteristic map, for example [16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

$P$-partition power sums

Aliniaeifard¹,

Wang²,

Willigenburg³

2021

Preprint

View full text Add to dashboard Cite

Motivated by the theory of P -partitions, we introduce the basis of combinatorial power sums for the Hopf algebra of quasisymmetric functions, refining the power sum symmetric functions. These share many properties with the type 1 and type 2 quasisymmetric power sums introduced by Ballantine, Daugherty, Hicks, Mason and Niese, and moreover expand into the monomial basis of quasisymmetric functions with nonnegative integer coefficients. We prove formulas for products, coproducts and classical quasisymmetric involutions via the combinatorics of P -partitions, and give combinatorial interpretations for the coefficients when expanded into the monomial and fundamental bases. Contents 1. Introduction 1 2. Preliminaries 2 3. Weighted P -partitions 5 4. Quasisymmetric and noncommutative power sums 9 5. The basis of combinatorial power sums 10 References 16

show abstract

Section: Quasisymmetric and Noncommutative Power Sumsmentioning

confidence: 98%

Section: The Basis Of Combinatorial Power Sumsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

$P$-partition power sums

Aliniaeifard¹,

Wang²,

Willigenburg³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…This space was defined in [7] by using P -partitions, which generates the fundamental quasisymmetric functions F α . In [4] the authors introduced two quasisymmetric powersum bases (i.e. a basis of QSym that refines p λ ) Φ and Ψ whose duals are the Φ and Ψ bases in NSym which was introduced in [6].…”

Section: Introductionmentioning

confidence: 99%

“…. , |γ l |) and I(α) = γ ′ 1 | • • • |γ ′ l .For example, I(1, 2, 1, 1) = (1, 1, 2, 1) and C(1, 2, 1, 1) =(1,4).…”

mentioning

confidence: 99%

Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables

Lazzeroni¹

2021

Preprint

View full text Add to dashboard Cite

We introduce new bases for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. These bases are expanded in terms of quasisymmetric monomial functions by using fillings of matrices. We define the analog of these bases in quasisymmetric functions of non-commuting variables. Our new bases have a (shifted) shuffle product and a deconcatenate coproduct. Finally, we describe a change of basis rule from the quasisymmetric powersum basis to the quasisymmetric fundamental basis.

show abstract

The Chromatic Quasisymmetric Class Function of a Digraph

White

2021

Ann. Comb.

View full text Add to dashboard Cite

On quasisymmetric power sums

Cited by 9 publications

References 12 publications

$P$-partition power sums

$P$-partition power sums

Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables

The Chromatic Quasisymmetric Class Function of a Digraph

Contact Info

Product

Resources

About