Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Aliniaeifard, Farid"'
We answer a question of Bergeron, Hohlweg, Rosas, and Zabrocki from 2006 to give a combinatorial description for the coproduct of the x-basis in the Hopf algebra of symmetric functions in noncommuting variables, NCSym, which arises in the theory of G
Externí odkaz:
http://arxiv.org/abs/2409.00177
Autor:
Aliniaeifard, Farid, Asgarli, Shamil, Esipova, Maria, Shelburne, Ethan, van Willigenburg, Stephanie, Whitehead, Tamsen
We show that the chromatic quasisymmetric function (CQF) of a labeled path graph on $n$ vertices is not symmetric unless the labeling is the natural labeling $1, 2, ..., n$ or its reverse $n, ..., 2, 1$. We also show that the star graph $K_{1, n-1}$
Externí odkaz:
http://arxiv.org/abs/2408.14455
We define vertex-colourings for edge-partitioned digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. We use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and
Externí odkaz:
http://arxiv.org/abs/2208.08458
We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating functions in the natural way and compute their product, coproduct and othe
Externí odkaz:
http://arxiv.org/abs/2112.06457
Autor:
Aliniaeifard, Farid, Thiem, Nathaniel
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This paper exa
Externí odkaz:
http://arxiv.org/abs/2111.03131
We define a graph Laplacian with vertex weights in addition to the more classical edge weights, which unifies the combinatorial Laplacian and the normalised Laplacian. Moreover, we give a combinatorial interpretation for the coefficients of the weigh
Externí odkaz:
http://arxiv.org/abs/2110.13949
Autor:
Aliniaeifard, Farid, Li, Shu Xiao
The peak algebra is originally introduced by Stembridge using enriched $P$-partitions. Using the character theory by Aguiar-Bergeron-Sottile, the peak algebra is also the image of $\Theta$, the universal morphism between certain combinatorial Hopf al
Externí odkaz:
http://arxiv.org/abs/2110.05648
We discover new linear relations between the chromatic symmetric functions of certain sequences of graphs and apply these relations to find new families of $e$-positive unit interval graphs. Motivated by the results of Gebhard and Sagan, we revisit t
Externí odkaz:
http://arxiv.org/abs/2108.04850
Publikováno v:
In Linear Algebra and Its Applications 15 June 2024 691:50-95
In 2004 Rosas and Sagan asked whether there was a way to define a basis in the algebra of symmetric functions in noncommuting variables, NCSym, having properties analogous to the classical Schur functions. This was because they had constructed a part
Externí odkaz:
http://arxiv.org/abs/2105.09964