Results 11 to 20 of about 2,701,787 (159)

Kromatic Quasisymmetric Functions [PDF]

The Electronic Journal of Combinatorics
We provide a construction for the kromatic symmetric function XG of a graph introduced by Crew, Pechenik, and Spirkl using combinatorial (linearly compact) Hopf algebras.
Marberg, Eric
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Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables [PDF]

The Electronic Journal of Combinatorics, 2022
We introduce a new $P$ basis for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. Unlike the quasisymmetric power sums of types 1 and 2, our basis is defined combinatorially: its expansion in quasisymmetric monomial ...
Lazzeroni, Anthony
core   +6 more sources

Eulerian quasisymmetric functions [PDF]

Advances in Mathematics, 2010
We introduce a family of quasisymmetric functions called Eulerian quasisymmetric functions, which specialize to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations of fixed cycle type ...
Shareshian, John, Michelle L. Wachs, John Shareshian, Wachs, Michelle L., Wachs, Michelle L   +4 more
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Fundamental quasisymmetric functions in superspace [PDF]

European Journal of Combinatorics
The fundamental quasisymmetric functions in superspace are a generalization of the fundamental quasisymmetric functions involving anticommuting variables.
Fishel, Susanna, Gatica, Jessica, Lapointe, Luc, Pinto, Maria Elena   +3 more
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Unimodality of Eulerian quasisymmetric functions [PDF]

Journal of Combinatorial Theory, Series A, 2011
We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and Eulerian polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j ...
Michelle L. Wachs, Anthony Henderson, Henderson, Anthony, Wachs, Michelle L., Wachs, Michelle L   +4 more
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Chromatic quasisymmetric functions [PDF]

Advances in Mathematics, 2016
We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric ...
Shareshian, John, Wachs, Michelle L
core   +3 more sources

A note on three types of quasisymmetric functions [PDF]

The Electronic Journal of Combinatorics, 2005
In the context of generating functions for P-partitions, we revisit three flavors of quasisymmetric functions: Gessel’s quasisymmetric functions, Chow’s type B quasisymmetric functions, and Poirier’s signed quasisymmetric functions.
T. Kyle Petersen
core   +7 more sources

Quasisymmetric Schur $Q$-functions and peak Young quasisymmetric Schur functions

Eur. J. Comb.
In this paper, we explore the relationship between quasisymmetric Schur $Q$-functions and peak Young quasisymmetric Schur functions. We introduce a bijection on $\mathsf{SPIT}(\alpha)$ such that $\{\mathrm{w}_{\rm c}(T) \mid T \in \mathsf{SPIT}(\alpha)\}$
Choi, Seung-Il, Nam, Sun-Young, Oh, Young-Tak   +2 more
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Peak quasisymmetric functions and Eulerian enumeration [PDF]

Advances in Mathematics, 2003
Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of cd-index, long studied in the context of ...
van Willigenburg, Stephanie, Billera, Louis J., Hsiao, Samuel K.   +2 more
core   +3 more sources

Quasisymmetric functions and Heisenberg doubles [PDF]

Journal of Algebra Combinatorics Discrete Structures and Applications, 2016
The ring of quasisymmetric functions is free over the ring of symmetric functions. This result was previously proved by M. Hazewinkel combinatorially through constructing a polynomial basis for quasisymmetric functions. The recent work by A. Savage and O.
Sun, Jie
core   +4 more sources