Poset cone and weighted P−partitions enumerator
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For a poset P on [n] we associate the poset cone C_P := cone{e_i − e_j : i <_P j}, where e_1, e_2, . . . , e_n are the standard basis vectors in R^n. The normal fan N(C_P) of this polyhedron is a coarsening of a subfan of the braid arrangement fan, given by hyperplanes {x_i = x_j}, for 1≤i<j≤n.
Weighted P−partitions enumerator F_q has an algebraic meaning as the universal
morphism from a certain combinatorial Hopf algebra of posets P to the Hopf algebra QSym of
quasisymmetric functions. For a well labelled poset P and q = 0 enumerator Fq specializes to the
classical Gessel's P−partitions enumerator. We also provide an example of posets with the same
P−partitions enumerators but which are distinguished by corresponding weighted quasisymmetric
enumerators.
Izvor:
Kongres mladih matematičara u Novom Sadu KMMNS2 Septembar, 29 – Oktobar, 1, 2022 Novi Sad, Srbija, 2022Kolekcije
Institucija/grupa
GraFarTY - CONF AU - Pešović, Marko PY - 2022 UR - https://grafar.grf.bg.ac.rs/handle/123456789/2704 AB - For a poset P on [n] we associate the poset cone C_P := cone{e_i − e_j : i <_P j}, where e_1, e_2, . . . , e_n are the standard basis vectors in R^n. The normal fan N(C_P) of this polyhedron is a coarsening of a subfan of the braid arrangement fan, given by hyperplanes {x_i = x_j}, for 1≤i<j≤n. Weighted P−partitions enumerator F_q has an algebraic meaning as the universal morphism from a certain combinatorial Hopf algebra of posets P to the Hopf algebra QSym of quasisymmetric functions. For a well labelled poset P and q = 0 enumerator Fq specializes to the classical Gessel's P−partitions enumerator. We also provide an example of posets with the same P−partitions enumerators but which are distinguished by corresponding weighted quasisymmetric enumerators. C3 - Kongres mladih matematičara u Novom Sadu KMMNS2 Septembar, 29 – Oktobar, 1, 2022 Novi Sad, Srbija T1 - Poset cone and weighted P−partitions enumerator UR - https://hdl.handle.net/21.15107/rcub_grafar_2704 ER -
@conference{ author = "Pešović, Marko", year = "2022", abstract = "For a poset P on [n] we associate the poset cone C_P := cone{e_i − e_j : i <_P j}, where e_1, e_2, . . . , e_n are the standard basis vectors in R^n. The normal fan N(C_P) of this polyhedron is a coarsening of a subfan of the braid arrangement fan, given by hyperplanes {x_i = x_j}, for 1≤i<j≤n. Weighted P−partitions enumerator F_q has an algebraic meaning as the universal morphism from a certain combinatorial Hopf algebra of posets P to the Hopf algebra QSym of quasisymmetric functions. For a well labelled poset P and q = 0 enumerator Fq specializes to the classical Gessel's P−partitions enumerator. We also provide an example of posets with the same P−partitions enumerators but which are distinguished by corresponding weighted quasisymmetric enumerators.", journal = "Kongres mladih matematičara u Novom Sadu KMMNS2 Septembar, 29 – Oktobar, 1, 2022 Novi Sad, Srbija", title = "Poset cone and weighted P−partitions enumerator", url = "https://hdl.handle.net/21.15107/rcub_grafar_2704" }
Pešović, M.. (2022). Poset cone and weighted P−partitions enumerator. in Kongres mladih matematičara u Novom Sadu KMMNS2 Septembar, 29 – Oktobar, 1, 2022 Novi Sad, Srbija. https://hdl.handle.net/21.15107/rcub_grafar_2704
Pešović M. Poset cone and weighted P−partitions enumerator. in Kongres mladih matematičara u Novom Sadu KMMNS2 Septembar, 29 – Oktobar, 1, 2022 Novi Sad, Srbija. 2022;. https://hdl.handle.net/21.15107/rcub_grafar_2704 .
Pešović, Marko, "Poset cone and weighted P−partitions enumerator" in Kongres mladih matematičara u Novom Sadu KMMNS2 Septembar, 29 – Oktobar, 1, 2022 Novi Sad, Srbija (2022), https://hdl.handle.net/21.15107/rcub_grafar_2704 .