Questions tagged [combinatorics]
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When was the parity of a permutation first understood?
In combinatorics, it is well understood that a permutation has a parity or sign: each permutation is either odd or even (sometimes described as negative and positive, respectively). Composing two ...
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Who discovered the famous combinatorial intepretation of Eulerian numbers?
Eulerian numbers $A(n, k)$ were discovered by Euler in 1755 in his work Institutiones calculi differentialis. In combinatorics, they count the number permutations of the numbers 1 to $n$ with exactly $...
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Who invented bit permutations like shuffle, butterfly and bit-reversal?
This question is about a class of periodic permutations,that are produced by applying finite permutations to the binary digits of all integers.
In lack of a better name, they shall be called bit ...
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What original mathematics arose from Jacquard loom and similar weaving devices?
Research mathematics is seldom directly applicable, but the questions we study are motivated by interplay with contemporary demands. As a combinatorialist, it's apparent that my field has benefited ...
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How was Pascal's triangle applied to fairly dividing the pot in an interrupted game?
Just wondering how Pascal used the triangle in the problem where they wanted to determine how to divide the pot when the game ended early. It was the first major probability problem conceived in ...
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Origin of Catalan numbers and original intuition of the first interpretation and proofs
I was reading about Catalan numbers and how they provide the number count in a variety of situations.
I found it very interesting how the main proof is about the underlying common patterns and ...
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Why are there relatively many Eastern European (specifically Hungarian) graph theorists?
I noticed that a large number of theories within graph theory are from Eastern European graph theorists, specifically Hungarian graph theorists. What is the relation between Eastern Europe (...
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Where did the Delannoy numbers make their first appearance?
I am writing a short exposition on the central Delannoy numbers and would like to find the year which Henri Delannoy first introduced them in a formal setting.
I believe Delannoy's initial ...
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Did Jacobi invent the Hungarian algorithm for the assignment problem over a century before Kőnig and Egerváry?
Wikipedia says:
In 2006, it was discovered that Carl Gustav Jacobi had solved the assignment problem in the 19th century, and the solution had been published posthumously in 1890 in Latin.
The ...
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Why are permutations ($_nP_r$) called differently in non-English languages ("variations" in German)?
First of all, you should be at least a little familiar with combinatorics to understand that question.
Some often used calculator keys in stochastic are the nCr and nPr ones.
Edit: I've first asked ...
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What is the origin of q-calculus notation?
It is kind of cute that q-analogues are used in physics (see this link for example), but it is also kind of confusing because the 'q' does not stand for 'quantum'. It predates that use!
So, where ...
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Was Riddell's formula really so late?
Riddell's formula for unlabeled graphs is a generating function transformation $$1 + B(x) = \exp \sum_{k=1}^\infty \frac{A(x^k)}{k}$$ which gives the number of graphs whose connected components have a ...
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F. Schoblik's announced ''ausführliche Darstellung": a lost wrong proof of the Four Color Theorem?
In (the AMS Chelsea Publishing version of) what is perhaps the first genuine textbook on graph theory ever, Dénes Kőnig on p. 28 gives the illustration
and the footnote
which when translated says
...
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Who first proved Rota' conjecture
In Wikipedia in article about Rota's conjecture it is written: “ A proof of the conjecture has been announced by Geelen, Gerards, and Whittle” . In Quanta magazine in article about mathematician June ...
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Newton , Binomial Series and Power Series , and James Gregory
After 2 month long search on the net, I was lucky enough to find a pdf on how Newton found the series for sine. It was a beautiful derivation mostly geometrical. But he used the Binomial Series.
Now ...
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Origin of diagrammatics illustrating the relation between cumulants and moments?
The exponential-log transformation of exponential generating functions (see OEIS A036040 and A127671) relate the classical cumulants to their associated moments.
Who were some of the first to ...
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