Kaliszewski, Ryan Lambright, Justin Skandera, Mark
Published in
Journal of Algebraic Combinatorics

We combinatorially describe entries of the transition matrices which relate monomial bases of the zero-weight space of the quantum matrix bialgebra. This description leads to a combinatorial rule for evaluating induced sign characters of the type A Hecke algebra Hn(q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackag...

Rusnak, Lucas J. Robinson, Ellen Schmidt, Martin Shroff, Piyush
Published in
Journal of Algebraic Combinatorics

Restrictions of incidence preserving path maps produce oriented hypergraphic All Minors Matrix-tree Theorems for Laplacian and adjacency matrices. The images of these maps produce a locally signed graphic, incidence generalization, of cycle covers and basic figures that correspond to incidence-k-forests. When restricted to bidirected graphs, the na...

Kashiwara, Masaki Oh, Se-jin
Published in
Journal of Algebraic Combinatorics

We prove that the Grothendieck rings of category CQ(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}^{(t)}_Q$$\end{document} over quantum affine algebras ...

Weber, Andrzej Zielenkiewicz, Magdalena
Published in
Journal of Algebraic Combinatorics

We study residue formulas for push-forward in the equivariant K-theory of homogeneous spaces. For the classical Grassmannian, the residue formula can be obtained from the cohomological formula by a substitution. We also give another proof using symplectic reduction and the method involving the localization theorem of Jeffrey–Kirwan. We review formu...

Gao, Suogang Li, Zengti Wu, Weili Pardalos, Panos M. Du, Dingzhu
Published in
Journal of Algebraic Combinatorics

In this paper, we give an overview of combinatorial group testing and algebra. Our survey focuses on the constructions with algebraic methods, especially geometry of classical groups over finite fields.

Cossidente, A. Pavese, F.
Published in
Journal of Algebraic Combinatorics

New families of Cameron–Liebler line classes of PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{PG}(3,q)$$\end{document}, q≥7\documentclass[12pt]{minimal...

Chen, Jiyong Jin, Wei Li, Cai Heng
Published in
Journal of Algebraic Combinatorics

A complete classification is given of 2-distance-transitive circulants, which shows that a 2-distance-transitive circulant is a cycle, a Paley graph of prime order, a regular complete multipartite graph, or a regular complete bipartite graph of order twice an odd integer minus a 1-factor.

Donati, Giorgio Durante, Nicola
Published in
Journal of Algebraic Combinatorics

Using a variation of Seydewitz’s method of projective generation of quadratic cones, we define an algebraic surface of PG(3,qn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docu...

Pan, Jiangmin Peng, Zhaofei
Published in
Journal of Algebraic Combinatorics

Edge-transitive graphs of order a prime or a product of two distinct primes with any positive integer valency, and of square-free order with valency at most 7 have been classified by a series of papers. In this paper, a complete classification is given of edge-transitive Cayley graphs of square-free order with valency less than the smallest prime d...

Gerber, Thomas
Published in
Journal of Algebraic Combinatorics

We explain how the action of the Heisenberg algebra on the space of q-deformed wedges yields the Heisenberg crystal structure on charged multipartitions, by using the Boson–Fermion correspondence and looking at the action of the Schur functions at q=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usep...