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Integrable Combinatorics [PDF]

open access: yesProceedings of the International Congress of Mathematicians (ICM 2018), 2012
We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)Comment: 21 pages, 16 figures, proceedings ...
Di Francesco, Philippe
core   +7 more sources

Combinatorics

open access: yesBicycle or Unicycle?, 2020
. It is known that the complex Grassmannian of k -dimensional sub-spaces can be identified with the set of projection matrices of rank k . It is also classically known that the convex hull of this set is the set of Hermitian matrices with eigenvalues ...
Peter Keevash   +2 more
semanticscholar   +4 more sources

Supersymmetry and Combinatorics [PDF]

open access: yesCommunications in Mathematical Physics, 2006
We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers.
Onofri, E., Veneziano, G., Wosiek, J.
core   +8 more sources

Portable Food‐Freshness Prediction Platform Based on Colorimetric Barcode Combinatorics and Deep Convolutional Neural Networks

open access: yesAdvanced Materials, 2020
Artificial scent screening systems (known as electronic noses, E‐noses) have been researched extensively. A portable, automatic, and accurate, real‐time E‐nose requires both robust cross‐reactive sensing and fingerprint pattern recognition.
Shu Wang, Ming Wang, Zequn Cui
exaly   +2 more sources

Rational Combinatorics

open access: yesAdvances in Applied Mathematics, 2007
We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.Comment: Adv. in Appl. Math.
Baez   +12 more
core   +9 more sources

Complexity problems in enumerative combinatorics [PDF]

open access: yesarXiv, 2018
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
I. Pak
arxiv   +3 more sources

Senior High School Students’ Higher Order Thinking Skills in Solving Combinatorics Problems

open access: yesJurnal Pendidikan Matematika, 2021
Higher Order Thinking Skills (HOTS) refer to students' ability to solve problems by analyzing, evaluating, and creating. HOTS are essential for 21st century learning. Solving combinatorics problem troubleshooting requires HOTS.
Arif Fatahillah   +2 more
exaly   +3 more sources

Combinatorics and connectionism

open access: bronzeDiscrete Mathematics, 1994
AbstractIn recent years there has been a great deal of interest in ‘connectionism’. This name covers a variety of activities, some of them wholly non-mathematical, concerned with processes which resemble the cognitive functions of the human brain. In this paper I shall use standard graph-theoretic terminology to describe some mathematical aspects of ...
Norman Biggs
openalex   +3 more sources

On the Combinatorics of Cumulants

open access: bronzeJournal of Combinatorial Theory, Series A, 2000
AbstractWe study cumulants by Umbral Calculus. Various formulae expressing cumulants by umbral functions are established. Links to invariant theory, symmetric functions, and binomial sequences are made.
Gian‐Carlo Rota, Jianhong Shen
openalex   +3 more sources

The combinatorics of splittability

open access: yesAnnals of Pure and Applied Logic, 2004
Marion Scheepers, in his studies of the combinatorics of open covers, introduced the property Split(U,V) asserting that a cover of type U can be split into two covers of type V. In the first part of this paper we give an almost complete classification of
Bartoszyński   +13 more
core   +5 more sources

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