Gnedin, Alexander Gorin, Vadim Kerov, Sergei
Published in
Journal of Algebraic Combinatorics

A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant algebra of \documentclass[12pt]{minimal} \usepackage{...

Cumplido, María
Published in
Journal of Algebraic Combinatorics

The minimal standardizer of a curve system on a punctured disk is the minimal positive braid that transforms it into a system formed only by round curves. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin–Tits groups of spherical type and we show that, to compute ...

Kang, Ming-Hsuan McCallum, Rupert
Published in
Journal of Algebraic Combinatorics

In the case where G=SL2(F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=\hbox {SL}_{2}(F)$$\end{document} for a non-archimedean local field F and Γ\documentclass[12...

Ryba, Christopher
Published in
Journal of Algebraic Combinatorics

Let k be an algebraically closed field of characteristic zero, and let C=R-mod\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {C}} = {\mathcal {R}} -\hbox {mo...

Gao, Xing Wang, Xiaomeng
Published in
Journal of Algebraic Combinatorics

Infinitesimal bialgebras were introduced by Joni and Rota. An infinitesimal bialgebra is at the same time an algebra and coalgebra, in such a way that the comultiplication is a derivation. Twenty years after Joni and Rota, Aguiar introduced the concept of an infinitesimal (non-unitary) Hopf algebra. In this paper, we study infinitesimal unitary bia...

Ghosh, Debarun Spallone, Steven
Published in
Journal of Algebraic Combinatorics

In Ayyer et al. (J Comb Theory Ser A 150:208–232, 2017), the authors characterize the partitions of n whose corresponding representations of Sn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...

Matsumura, Tomoo
Published in
Journal of Algebraic Combinatorics

We show that the flagged Grothendieck polynomials defined as generating functions of flagged set-valued tableaux of Knutson et al. (J Reine Angew Math 630:1–31, 2009) can be expressed by a Jacobi–Trudi-type determinant formula generalizing the work of Hudson–Matsumura (Eur J Comb 70:190–201 2018). We also introduce the flagged skew Grothendieck pol...

Clark, Pete L.
Published in
Journal of Algebraic Combinatorics

We present a generalization of Warning’s second theorem to polynomial systems over a finite local principal ring with restricted input and relaxed output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new proof of that result). Applications to additive group theory, graph theory and polynomial interpolation are pur...

Csajbók, Bence Siciliano, Alessandro
Published in
Journal of Algebraic Combinatorics

We investigate punctured maximum rank distance codes in cyclic models for bilinear forms of finite vector spaces. In each of these models, we consider an infinite family of linear maximum rank distance codes obtained by puncturing generalized twisted Gabidulin codes. We calculate the automorphism group of such codes, and we prove that this family c...

Nguyen, Viet Anh
Published in
Journal of Algebraic Combinatorics

We prove two explicit formulae for one-part double Hurwitz numbers with completed 3-cycles. We define “combinatorial Hodge integrals” from these numbers in the spirit of the celebrated ELSV formula. The obtained results imply some explicit formulae and properties of the combinatorial Hodge integrals.