permutation - Enumeration of distinct events in R -

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i searching general approach enumerate sequence associated following problem , deposit results in 3 dimensional matrix in r.

i think there must combinatorial solution have been unable find one. hopefully, detailed below sufficiently characterize problem. welcomed.

given there n periods , c distinct areas in occurrence of event e must occur once in each area, enumeration of possible sequences?

for example, if there 3 time periods {1,2,3} , 2 areas {a,b}, manually enumerating solutions gives:

period 1    2    3 area   b  b  b sol 1  e e  - -  - -   ; ie event occurs in both areas @ time 1, nothing happens @ time 2 , 3 sol 2  - -  e e  - -   ; event occurs in both areas @ time 2 etc sol 3  - -  - -  e e sol 4  e -  - e  - - sol 5  e -  - -  - e sol 6  - e  e -  - - sol 7  - e  - -  e - sol 8  - -  e -  - e sol 9  - -  - e  e -

regardless of number of areas , number of time steps, know number of solutions n^c. case 3 ways event occur in 'a' times 3 ways event occur in 'b', 3 x 3 = 9 distinct sequences. said, wish implement generalized solution number of periods , number of areas , store result in matrix indexed [time][area][sequence]. thanks!

many thanks. believe following working correctly.

# solution: numperiods <- 4 numevents <- 2 numseqs <- numperiods^numevents  gridparam <- rep(list(seq(numperiods)),numevents) g <- as.matrix(expand.grid(gridparam)) print(g)  m <- t(apply(g, 1,           function(z) {             x <- rep(0, numperiods*numevents)              (i in 1:numseqs)              {               x[numevents * z[i] - (numevents-i)] <- 1             }             x          })) print(m)  result <- array(m,c(numseqs,numevents,numperiods)) colnames(result) <- outer("event",1:numevents, paste) rownames(result) <- outer("seq", 1:numseqs, paste) # time period third dim print(result)

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