Re: beyond http://1stworks.com much-acclaimed 'breakthrough'binomial QI : Enumerative Combinatorics multinomial UNLIMITED 'nested multiple constraints' lexicographic ranked index Lattice Paths

On 7 June, 17:12, biject <biject.b...@xxxxxxxxx> wrote:

�Actually its much stronger trying to compress every
combination to some fixed number of bits

take 4 bits for example.

that is 16 possible strings

you can map 8 to every 3 bits
you can map 4 to every 2 bits
you can map 2 to every 1 bits
you can even map 1 more to the NULL case or empty file

but that still only adds up to 15 sadly you are stuck
with one case that has no where to go.

yes the earlier mentioned exact 1 single instance 'pigeonhole counting
theorem refutation' of all 2^M -1 possible combinations of known
constant fixed M bits input

as mentioned this one EXITS case can be assigned to all '1's ie
'111...11' which could very convenient be transmitted conveyed as M #
of '1's with log(base2)M bits costs , or even just send as '111...11'
M bits costs ( not even > M bits costs )

days practicalities common useful to know of expects fixed constant M
filesize transmissions ( different people may use different value of
M ), for repeat many many multiple use even if includes this log(base2)
M bits fixed costs initially , this costs -> infinitesimal small over
repeated use over & over again ..... theoretics wise is an entirely
different matter altogether

a very large filesize R ( R multiples of M ) can be split into R/M #
of BLOCKS of M bits


Worse yet if you want to be able to compress
4 bits and 5bits each to a lower string you
still have one exta case at 4 bits that has
not been taken care of so then your stuck with
that and many more from the 5 bits case since
they have been used when trying to make the
4 case smaller.


as mentioned theoretics wise much of what been said are right ....

(?) but think here if compresses 5 bits it doesn't matter what earlier
4 bits does with the 3 bits 2 bits 1 bit 0 bit , 5 bits will EXIT on
exception's all 5 '1's otherwise will continue compresses uses 4 bits
3bits 2bits 1 bit 0 bit ( here again smaller 4 bits if all 4 '1's
will EXIT , smaller 3 bits if all 3 '1's will EXIT , smaller 2 bits if
all 2 '1's will EXIT , smaller 1 bits if all 1 '1' will EXIT )


compression at its best it nothing more than
reordering strings. Some map to smaller some
map to longer strings. We only call it compression
based on the hope that the transformation
we use is good for the small subset of files
that people find useful.

theoretics wise perfect TRUE

days practicalities ( knowing frequent usage filesize/ block size M )
if mapped to longer strings > M can just send original input M
instead


�When testing general compressors. If the code
can actually compress some files to a smaller
size. You can always find �a larger number
files it will expand to a larger size.

�So a test could be rigged to make any compressor
look bad

yes

however for days practicalities ( knowing frequent usage filesize/
block size M ) if mapped to longer strings > M can just send original
input M instead
.

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