Results 41 to 50 of about 143,013 (228)

Combinatorics of Chord Progressions [PDF]

, 2012
Color poster with text and diagrams.This study explored an overlap between combinatorics and music. The goal was to show chord progressions that are common to a specific collection of music, composer, or era.University of Wisconsin--Eau Claire Office of
Kiefer, Peter
core   +1 more source

Puzzling the 120-cell

, 2015
We introduce Quintessence: a family of burr puzzles based on the geometry and combinatorics of the 120-cell. We discuss the regular polytopes, their symmetries, the dodecahedron as an important special case, the three-sphere, and the quaternions. We then
Schleimer, Saul, Segerman, Henry
core   +1 more source

The implications of generative artificial intelligence for mathematics education

School Science and Mathematics, EarlyView.
Abstract Generative artificial intelligence has become prevalent in discussions of educational technology, particularly in the context of mathematics education. These AI models can engage in human‐like conversation and generate answers to complex questions in real‐time, with education reports accentuating their potential to make teachers' work more ...
Candace Walkington
wiley   +1 more source

Trace Identities for the Topological Vertex

, 2017
The topological vertex is a universal series which can be regarded as an object in combinatorics, representation theory, geometry, or physics. It encodes the combinatorics of 3D partitions, the action of vertex operators on Fock space, the Donaldson ...
Bryan, Jim, Kool, Martijn, Young, Benjamin   +2 more
core   +1 more source

Combinatorics of diagrams of permutations [PDF]

Discrete Mathematics & Theoretical Computer Science, 2014
There are numerous combinatorial objects associated to a Grassmannian permutation $w_λ$ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and their q-analogues in the case of permutations $\mathcal{w}$ that are not necessarily Grassmannian.
Alejandro H. Morales, Joel Brewster Lewis   +1 more
openaire   +6 more sources

The weak Lefschetz property for artinian Gorenstein algebras

Bulletin of the London Mathematical Society, EarlyView.
Abstract It is an extremely elusive problem to determine which standard artinian graded K$K$‐algebras satisfy the weak Lefschetz property (WLP). Codimension 2 artinian Gorenstein graded K$K$‐algebras have the WLP and it is open to what extent such result might work for codimension 3 artinian Gorenstein graded K$K$‐algebras.
Rosa M. Miró‐Roig
wiley   +1 more source

The Combinatorics of Iterated Loop Spaces

, 2003
It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads.
Batanin, M. A.
core   +1 more source

Normal covering numbers for Sn$S_n$ and An$A_n$ and additive combinatorics

Bulletin of the London Mathematical Society, EarlyView.
Abstract The normal covering number γ(G)$\gamma (G)$ of a noncyclic group G$G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for γ(Sn)$\gamma (S_n)$ and γ(An)$\gamma (A_n)$ depending on the arithmetic structure of n$n$. In particular we determine the limsups over γ(Sn)/n$\gamma (S_n) / n$ and γ(An)
Sean Eberhard, Connor Mellon
wiley   +1 more source

Indiscernibles in monadically NIP theories

Bulletin of the London Mathematical Society, EarlyView.
Abstract We prove various results around indiscernibles in monadically NIP theories. First, we provide several characterizations of monadic NIP in terms of indiscernibles, mirroring previous characterizations in terms of the behavior of finite satisfiability. Second, we study (monadic) distality in hereditary classes and complete theories.
Samuel Braunfeld, Michael C. Laskowski
wiley   +1 more source

Estimates on the decay of the Laplace–Pólya integral

Bulletin of the London Mathematical Society, EarlyView.
Abstract The Laplace–Pólya integral, defined by Jn(r)=1π∫−∞∞sincntcos(rt)dt$J_n(r) = \frac{1}{\pi }\int _{-\infty }^\infty \operatorname{sinc}^n t \cos (rt) \,\mathrm{d}t$, appears in several areas of mathematics. We study this quantity by combinatorial methods; accordingly, our investigation focuses on the values at integer rs$r{\rm s}$.
Gergely Ambrus, Barnabás Gárgyán
wiley   +1 more source