Three combinatorial formulas for type $A$ quiver polynomials and $K$ -polynomials

Lots of research focuses on the combinatorics behind various bases of cluster algebras. This paper studies the natural basis of a type $A$ cluster algebra, which consists of all cluster monomials. We introduce a new kind of combinatorial formula for the cluster monomials in terms of the so-called globally compatible collections. We give bijective proofs of these formulas by comparing with the well-known combinatorial models of the $T$-paths and of the perfect matchings in a snake diagram. For cluster variables of a type $A$ cluster algebra, we give a bijection that relates our new formula with the theta functions constructed by Gross, Hacking, Keel and Kontsevich.

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Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2695 ◽

2009 ◽

Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽

Author(s):

Cristian Lenart

Keyword(s):

Weyl Group ◽

Type A ◽

Macdonald Polynomials ◽

Combinatorial Formula ◽

Young Diagrams ◽

Affine Weyl Group ◽

Littlewood Polynomials ◽

Combinatorial Formulas ◽

International Audience ◽

Type C

International audience A breakthrough in the theory of (type $A$) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of fillings of Young diagrams. Recently, Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of the corresponding affine Weyl group. In this paper, we show that a Haglund-Haiman-Loehr type formula follows naturally from the more general Ram-Yip formula, via compression. Then we extend this approach to the Hall-Littlewood polynomials of type $C$, which are specializations of the corresponding Macdonald polynomials at $q=0$. We note that no analog of the Haglund-Haiman-Loehr formula exists beyond type $A$, so our work is a first step towards finding such a formula.

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Biological and Morphological Studies on Low-Leukemia-Strain Mice with Hodgkin's-Like Neoplasia Induced by Serial Cell-Free Transmission of Leukemic Organs of SJL/J Strain Mice

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100792 ◽

1968 ◽

Vol 26 ◽

pp. 210-211

Author(s):

S. Fujinaga ◽

K. Maruyama ◽

C.W. Williams ◽

K. Sekhri ◽

L. Dmochowski

Keyword(s):

Tissue Culture ◽

Type A ◽

Reticulum Cell ◽

Type B ◽

Viral Origin ◽

Serial Transfer ◽

Strain Mouse ◽

Morphological Studies ◽

Cell Neoplasm ◽

Free Material

Yumoto and Dmochowski (Cancer Res.27, 2098 (1967)) reported the presence of mature and immature type C leukemia virus particles in leukemic organs and tissues such as lymph nodes, spleen, thymus, liver, and kidneys of SJL/J strain mice with Hodgki's-like disease or reticulum cell neoplasm (type B). In an attempt to ascertain the possibility that this neoplasia may be of viral origin, experiments with induction and transmission of this neoplasm were carried out using cell-free extracts of leukemic organs from an SJL/J strain mouse with spontaneous disease.It has been possible to induce the disease in low-leukemia BALB/c and C3HZB strain mice and serially transfer the neoplasia by cell-free extracts of leukemic organs of these mice. Histological examination revealed the neoplasia to be of either reticulum cell-type A or type B. Serial transfer is now in its fifth passage. In addition leukemic spleen from another SJL/J strain mouse with spontaneous reticulum cell neoplasm (type A) was set up in tissue culture and is now in its 141st serial passage in vitro. Preliminary results indicate that cell-free material of 39th tissue culture passage can reproduce neoplasia in BALB/c mice.

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Hepatitis A Antigen in Liver, Bile and Stool

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100115328 ◽

1975 ◽

Vol 33 ◽

pp. 340-341

Author(s):

D.R. Jackson ◽

J.H. Hoofnagle ◽

A.N. Schulman ◽

J.L. Dienstag ◽

R.H. Purcell ◽

...

Keyword(s):

Hepatitis A ◽

Liver Enzymes ◽

Hepatitis A Virus ◽

Type A ◽

Initial Study ◽

Virus Like Particle ◽

Elevated Liver Enzymes ◽

Ag Particles ◽

Ag Particle ◽

Human Stool

Using immune electron microscopy Feinstone et. al. demonstrated the presence of a 27 nm virus-like particle in acute-phase stools of patients with viral hepatitis, type A, These hepatitis A antigen (HA Ag) particles were aggregated by convalescent serum from patients with type A hepatitis but not by pre-infection serum. Subsequently Dienstag et. al. and Maynard et. al. produced acute hepatitis in chimpanzees by inoculation with human stool containing HA Ag. During the early acute disease, virus like particles antigenically, morphologically and biophysically identical to the human HA Ag particle were found in chimpanzee stool. Recently Hilleman et. al. have described similar particles in liver and serum of marmosets infected with hepatitis A virus (HAV). We have investigated liver, bile and stool from chimpanzees and marmosets experimentally infected with HAV. In an initial study, a chimpanzee (no.785) inoculated with HA Ag-containing stool developed elevated liver enzymes 21 days after exposure.

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Detection of Viral Antigens in Mouse and Rat Tumor Cells by Immunoelectron Microscopy Following Periodate-Lysine-Paraformaldehyde (PLP) Fixation

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010009124x ◽

1976 ◽

Vol 34 ◽

pp. 252-253

Author(s):

Y. Ohtsuki ◽

G. Seman ◽

J. M. Bowen ◽

M. Scanlon ◽

L. Dmochowski

Keyword(s):

Immunoelectron Microscopy ◽

Mammary Tumor ◽

Type A ◽

Rabbit Serum ◽

Virus Particles ◽

Viral Antigens ◽

Culture Cells ◽

Mouse Mammary Tumor ◽

Tumor Virus ◽

Immunoperoxidase Labeling

Recently, periodate-lysine-paraformaldehyde (PLP) fixation was reported for immunoelectron microscopy (1). In PLP fixation, carbohydrates are oxidized by periodate and cross-linked by lysine; paraformaldehyde stabilizes proteins and lipids. By using PLP fixation, intracytoplasmic type A viral antigens have been previously demonstrated by immunoperoxidase labeling (2). In the present study, PLP fixation has been applied for the detection of the same antigens in mouse mammary tumor culture cells by both immunoferritin and immunoperoxidase methods. Rabbit anti-intracytoplasmic type A virus serum (anti-A), kindly provided by Dr. M. Muller (3), rabbit anti-strain A mouse mammary tumor virus (anti-MMTV) and preimmune rabbit serum as control were used to detect viral antigens in cells of C3H/HeJ strain mouse mammary tumor culture. Attempts have been also made to demonstrate peroxidase labeling of type C virus particles in frozen sections of an SD-MSV-induced NZB rat bone tumor tissue by rabbit anti-MuLV serum.

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