789 research outputs found
Regular Schur labeled skew shape posets and their 0-Hecke modules
Assuming Stanley's -partition conjecture holds, the regular Schur labeled
skew shape posets with underlying set are precisely the
posets such that the -partition generating function is symmetric and the
set of linear extensions of , denoted , is a left weak Bruhat
interval in the symmetric group . We describe the permutations
in in terms of reading words of standard Young tableaux when
is a regular Schur labeled skew shape poset, and classify 's up to
descent-preserving isomorphism as ranges over regular Schur labeled skew
shape posets. The results obtained are then applied to classify the -Hecke
modules associated with regular Schur labeled skew shape posets
up to isomorphism. Then we characterize regular Schur labeled skew shape
posets as the posets whose linear extensions form a dual plactic-closed subset
of . Using this characterization, we construct distinguished
filtrations of with respect to the Schur basis when is a
regular Schur labeled skew shape poset. Further issues concerned with the
classification and decomposition of the -Hecke modules are
also discussed.Comment: 44 page
Poset modules of the -Hecke algebras and related quasisymmetric power sum expansions
Duchamp--Hivert--Thibon introduced the construction of a right
-module, denoted as , for any partial order on the set .
This module is defined by specifying a suitable action of on the set
of linear extensions of . In this paper, we refer to this module as the
poset module associated with . Firstly, we show that has a Hopf algebra structure that is isomorphic to the
Hopf algebra of quasisymmetric functions, where is the full
subcategory of whose objects are direct sums of finitely
many isomorphic copies of poset modules and is the
Grothendieck group of . We also demonstrate how
(anti-)automorphism twists interact with these modules, the induction product
and restrictions. Secondly, we investigate the (type 1) quasisymmetric power
sum expansion of some quasi-analogues of Schur functions, where
is a composition. We show that they can be expressed as the sum of the
-partition generating functions of specific posets, which allows us to
utilize the result established by Liu--Weselcouch. Additionally, we provide a
new algorithm for obtaining these posets. Using these findings, for the dual
immaculate function and the extended Schur function, we express the
coefficients appearing in the quasisymmetric power sum expansions in terms of
border strip tableaux.Comment: 42 page
Temperature dependence of Mott transition in VO_2 and programmable critical temperature sensor
The temperature dependence of the Mott metal-insulator transition (MIT) is
studied with a VO_2-based two-terminal device. When a constant voltage is
applied to the device, an abrupt current jump is observed with temperature.
With increasing applied voltages, the transition temperature of the MIT current
jump decreases. We find a monoclinic and electronically correlated metal (MCM)
phase between the abrupt current jump and the structural phase transition
(SPT). After the transition from insulator to metal, a linear increase in
current (or conductivity) is shown with temperature until the current becomes a
constant maximum value above T_{SPT}=68^oC. The SPT is confirmed by micro-Raman
spectroscopy measurements. Optical microscopy analysis reveals the absence of
the local current path in micro scale in the VO_2 device. The current uniformly
flows throughout the surface of the VO_2 film when the MIT occurs. This device
can be used as a programmable critical temperature sensor.Comment: 4 pages, 3 figure
In Vitro Chemosensitivity Using the Histoculture Drug Response Assay in Human Epithelial Ovarian Cancer
The choice of chemotherapeutic drugs to treat patients with epithelial ovarian cancer has not depended on individual patient characteristics. We have investigated the correlation between in vitro chemosensitivity, as determined by the histoculture drug response assay (HDRA), and clinical responses in epithelial ovarian cancer. Fresh tissue samples were obtained from 79 patients with epithelial
ovarian cancer. The sensitivity of these samples to 11 chemotherapeutic agents was tested using the HDRA method according to established methods, and we analyzed the results retrospectively. HDRA showed that they were more chemosensitive to carboplatin, topotecan and belotecan, with inhibition rates of 49.2%, 44.7%, and 39.7%, respectively, than to cisplatin, the traditional drug of choice in epithelial ovarian cancer. Among the 37 patients with FIGO stage Ⅲ/Ⅳ serous adenocarcinoma
who were receiving carboplatin combined with paclitaxel, those with carboplatin-sensitive samples on HDRA had a significantly longer median disease-free interval than patients with carboplatin-
resistant samples (23.2 vs. 13.8 months, p<0.05), but median overall survival did not differ significantly
(60.4 vs. 37.3 months, p=0.621). In conclusion, this study indicates that HDRA could provide useful information for designing individual treatment strategies in patients with epithelial ovarian cancer
The projective cover of tableau-cyclic indecomposable -modules
Let be a composition of and a permutation in
. This paper concerns the projective covers of
-modules , and
, which categorify the dual immaculate
quasisymmetric function, the extended Schur function, and the quasisymmetric
Schur function when is the identity, respectively. First, we show that
the projective cover of is the projective indecomposable
module due to Norton, and and the -twist
of the canonical submodule of
for 's satisfying suitable
conditions appear as -homomorphic images of .
Second, we introduce a combinatorial model for the -twist of
and derive a series of surjections starting from
to the -twist of
. Finally, we construct the projective
cover of every indecomposable direct summand of
. As a byproduct, we give a characterization of
triples such that the projective cover of
is indecomposable.Comment: 41 page
Homological properties of 0-Hecke modules for dual immaculate quasisymmetric functions
Let be a nonnegative integer. For each composition of , Berg
introduced a cyclic indecomposable -module
with a dual immaculate quasisymmetric function as the
image of the quasisymmetric characteristic. In this paper, we study
's from the homological viewpoint. To be precise, we
construct a minimal projective presentation of and a
minimal injective presentation of as well. Using them, we
compute and , where is
the simple -module attached to a composition of . We also
compute when
and , where represents the lexicographic
order on compositions.Comment: 44 pages, to be published in Forum of Math: Sigm
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