We reduce the problem of determining the maximum number of permutations of a finite set such that any pair of permutations has at least t common transpositions to the problem of determining the maximum number of permutations of finite set such that any pair has at least t common fixed points....
This problem was asked in recent CodeNation Online Test — Please give your solution idea to it Given A,B,C — Count the number of valid arrays of size "A"; such that each number of the array is in the range [1,C]; and no subarray of length > B exists in the valid array such...
Mathematics - CombinatoricsA conjecture widely attributed to Neumann is that all finite non-desarguesian projective planes contain a Fano subplane. In this note, we show that any finite projective plane of even order which admits an orthogonal polarity contains a Fano subplane. The number of ...
Large language model improves on efforts to solve combinatorics problems inspired by the card game Set. By Davide Castelvecchi Twitter Facebook Email The card game Set has long inspired mathematicians to create interesting problems.Access options Access through your institution Access Nature and 54 ...
For more than 250 years combinatorial problems on chessboards have been studied and published in numerous books on recreational mathematics. Two problems of this type include the problem of finding a placement of n non-attacking queens on an n×n chessboard and the problem of determining the mini...
T.P. Kirkman On a problem in combinatorics Cambridge Dublin Math. J., 2 (1847), pp. 191-204 Google Scholar [19] D.E. Knuth Dancing links J. Davies, B. Roscoe, J. Woodcock (Eds.), Millennial Perspectives in Computer Science, Palgrave Macmillan, Basingstoke (2000), pp. 187-214 Googl...
(n). While the proof of Mantel’s theorem is a simple combinatorial exercise, triangle-free graphs act as a kind of theoretical lodestone in extremal combinatorics: many important extremal tools or problems are first developed or studied in the context of triangle-free graphs. One may think, ...
Mathematics - Combinatorics52C995A99In this short note we apply a recent theorem of Koll\\'ar about the arithmeticgenus of curves to give a bound on the number of joints weighted by themultiplicities. This gives an affirmative answer to a conjecture of Carbery inthe generic case....
We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdos-Heilbronn problem in Additive Combinatorics. We formulate an open conjecture concerning the inverse Erdos-Heilbronn problem in nonabelian groups. We extend an inverse to the Dias ...
Mathematics - CombinatoricsWe completely resolve the boundary value problem for differential forms and conformally Einstein infinity in terms of the dual Hahn polynomials. Consequently, we produce explicit formulas for the Branson-Gover operators on Einstein manifolds and prove their representation as a ...