Permutations

2 artículos

100 prisoners problem 15 puzzle Aiguillette Antisymmetrizer Artin tits group Baxter permutation Bender knuth involution Block Borel fixed point theorem Box braids Braid theory Braided monoidal category Braiding machine Braids links and mapping class groups Change ringing Character variety Circular permutation in proteins Claw free permutation Cocompact group action Cornrows Costas array Covering groups of the alternating and symmetric groups Crochet braids Cycle notation Cycles and fixed points Deck mate Derangement Die reihe Discrepancy of permutations Duration series Elements of music Elsv formula Equivariant cohomology Equivariant topology Erd's szekeres theorem Faro shuffle Fingerloop braid Fisher yates shuffle Flow Formula composition Fourrag re French braid Fulani braids Galloon Gassmann triple Generalized symmetric group German armed forces badge of marksmanship Ghost leg Gilbert shannon reeds model Gilbreath shuffle Gimli Golomb dickman constant Gripfid Group actions in computational anatomy Group based cryptography Halls universal group Heaps algorithm Hurwitz braid group In place matrix transposition Infantry shoulder cord Kendall tau distance Koroba Kumihimo L vy steinitz theorem Lanyard Layered permutation Loop braid group Lucet Major index Mantel test Marudai Matsumotos theorem Method ringing Momentum map Multiply transitive group Multiply transitive group action Nubian wig Onan scott theorem Orbifold Orbit Order statistic Out shuffle Parastatistics Parker vector Perfect shuffle Permutation automaton Permutation box Permutation class Permutation pattern Permutation polynomial Pigtail Place permutation action Plain hunt Ply split braiding Principal bundle Process music Pseudorandom permutation Queue Random number Random permutation Retrograde inversion Riemann series theorem Riffle shuffle permutation Ring of symmetric functions Robinson schensted correspondence Robinson schensted knuth correspondence Russian braid Schreier vector Separable permutation Serialism Shuffling Shuffling machine Skew and direct sums of permutations Skew merged permutation Spherical braid group Sprang Stack sortable permutation Stanley wilf conjecture Steinhaus johnson trotter algorithm Substitution permutation network Superpattern Takadai Temperley lieb algebra Time point Tompkins paige algorithm Transposition Tressoir Veronese bell ringing Vexillary permutation Wedding cord Who cares if you listen Young symmetrizer Zassenhaus group

Combinatorics & Discrete Math BachilleratoAnálisis10 min

Nine Digits, Four Windows, and a Middle That Cannot Move

Nine slots hold the digits 1 to 9 and four overlapping windows each add to 20. One subtraction pins the centre digit to 5 with no search at all, and the same structure classifies every arrangement: there are 96 of them, falling into 48 mirror pairs. Change the target and the centre is forced to an odd digit that sometimes admits nothing.

Combinatorics & Discrete Math BachilleratoExplicación9 min

One in Three, and the Card That Was Never in the Problem

Wind appears nowhere in the winning condition, so delete it: three cards in six equally likely orders, and you win in the two where fire comes last. One in four is the correct probability that fire is last of all four cards, a strictly smaller event, and the gap is exactly one twelfth.