Fear, David Wanless, Ian M.
Published in
Journal of Algebraic Combinatorics

An orthomorphism over a finite field F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}$$\end{document} is a permutation θ:F↦F\documentclass[12pt]{minimal} ...

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...

Dimakis, Panagiotis Yue, Guangyi
Published in
Journal of Algebraic Combinatorics

In this paper, we define the combinatorial wall-crossing transformation and the generalized column regularization on partitions and prove that a certain composition of these two transformations has the same effect on the one-row partition (n). As corollaries we explicitly describe the quotients of the partitions which arise in this process. We also...

Castro, Francis N. Medina, Luis A. Sepúlveda, L. Brehsner
Published in
Journal of Algebraic Combinatorics

Exponential sums have applications to a variety of scientific fields, including, but not limited to, cryptography, coding theory and information theory. Closed formulas for exponential sums of symmetric Boolean functions were found by Cai, Green and Thierauf in the late 1990s. Their closed formulas imply that these exponential sums are linearly rec...

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...