Improve software to find combination lexicographical order

Improvements to NthIndex, the first standalone software program to calculate or find the lexicographic order or rank of a lotto combination; or find the combination for a given rank.

Posted by Ion Saliu on July 10, 2001.

In Reply to: Find index of lotto combination and vice versa posted by Ion Saliu on July 07, 2001.

• New version: 1.1, July 10, 2001.

Apparently, the first version of the lexicographic algorithm caused some errors on some PCs. There was a DOS configuration conflict. Probably the new version will be error-free. It is recommended to run the program at the DOS (command) prompt, not inside Windows.

There is another change in NTHINDEX. The new default for option: “Find Combination of Index L” is ‘the half point of total combinations in the lotto set’. For example, the ‘half point’ in a lotto 49/6 game is 6991908 (13983816 / 2). The corresponding combination is: 6-7-16-28-48. Check it out, if you play a 49/6 lotto game. In a PowerBall 49/5/42 game, the ‘half point’ is 40044564; the corresponding combination is: 7-8-28-30-46;42.

One more “point”: type the index without commas or dots! You get an error if you type the index as 40,044,564 or 40.044.564.

Other changes to the program in the form of ‘customizations’ are not available at this time.

Ion Saliu

This is a comprehensive list of my writings on the topic of lexicographical order or indexing, including algorithms and software.

• Lexicographic, lexicographical order, index, rank of permutations, exponential sets, combinations.
  This is the most intuitive, if not the best, introduction to the apparently difficult concept of lexicographic ordering (or indexing).

• Lexicographical Order: Lotto, Powerball, Mega Millions, Euromillions.
  This is the most comprehensive and intuitive presentation of the concept of lexicographic ordering (or indexing), including the superior software to tackle the task.

• Combination sequence number or Lexicographic Order Fast Algorithm.
  This is how it all started. I responded to challenges in various newsgroups. I came up with the complementary algorithm to the original algorithm by B.P. Buckles and M. Lybanon" (algorithm ACM #515). I offered my lexicographic algorithm bona fide to ACM. A bunch of suckers there tried to make my algorithm look like their creation, not mine!

• Combination Lexicographic Order, Rank, Index: The Comprehensive and Fast Algorithm.
  I expanded the lexicographical index concept to two-in-one games, particularly the U.S. lotto game of Powerball (applicable to Mega Millions as well).

• Calculate the combination lexicographic order of lotto data files.
  The introduction of DrawIndex, the software that calculates the lexicographic indexes for every combination (draw) in a lotto results file.

  The following are older and somehow outdated materials I wrote on lexicographical order subjects. Most of the older software is outdated. Nothing (in the whole world) can beat LexicographicSets or DrawIndex. Sentimentalism is good only to a close extent.
  

• Index, rank lexicographic order lotto combination.
• Combination sequence number or Lexicographic Order Debates.

Of course, everybody loves to feast on great software, especially when it is free! My combinatorics software (and other categories) is absolutely free to run, for an unlimited period of time. However, only the registered members have a right to download the software. Membership requires a nominal fee — the most reasonable there is to connect to the greatest and most useful software ever created. No kidding! Read the conditions to becoming a registered member: Download Great Free Software: Paid Membership Required.

• Software: Science, Mathematics, Statistics, Lexicographic, Combinatorial
  LexicographicSets, the universal permutations, arrangements and combinations lexicographic indexing (ranking);
  DrawIndex - highly automated lexicographical indexing for lotto draw files.
  NthIndex ~ lexicographic indexing superseded by LexicographicSets;
  SEQUENCE ~ lexicographic indexing superseded by LexicographicSets;
  COLORDER - lexicographical indexing for lotto and Powerball only;
  PermuteCombine, the universal permutations, arrangements and combinations generator for any numbers and words;
  Combinations, the universal combinations generator for any lotto, Keno, Powerball game: N numbers taken M at a time, in K steps;
  WRITER, random generator of letters to words, passwords, sentences.

Comments:
: : Improve software to find combination lexicographical order. Mathematics algorithm, formula, software, programs to generate calculate combination index, lexicographical order. Find combination, combinations, combinatorics formula formulas algorithm algorithms lexicographical order combination sequence number mathematics math maths lotto lottery. Combine odds, calculate odds, formulae to generate combinations. Free generator, function, software, freeware, program of lexicographical order or indexing or ordering. Theory of probability itself wouldn't have been possible without the science of combinations. Study, analysis of "Algorithm, algorithms, formula, formulas, formulae, math, mathematics to calculate combination index, order, index, lexicographic, lexicographical." Two major difficulties in combinatorics are related to two factors: 1) determining theoretically the rank (or lexicographical order) of a given combination; 2) constructing theoretically the combination of a given rank or combination sequence number. The first attempt to address the major issues came in 1974. B.P. Buckles and M. Lybanon created a computer program to construct a combination when the rank is known (algorithm "ACM #515"). It is a great achievement. The authors of that algorithm, however, were unable to reverse the procedure and determine the rank for a given combination. I wrote the computer program SEQUENCE. I presented the core of my algorithm in the message: 348.html Combination sequence number" or "Lexicographic Order" Fast Algorithm. My algorithm did not cover an important combinatorics field: PowerBall. The two major issues were so difficult that nobody came even close to solving them. I took a superficial look at the issues. Did Lexicographic, lex or analysis of algorithm, algorithms, formula, formulas, formulae, math, mathematics to calculate combination index, order, index, lexicographic, lexicographical order. I "saw' the invisible PowerBall algorithm in a late dream. I tried to implement it several times, to no avail. I wrote the algorithm invisibly, in a dream. When I woke up I found a compiled program already. It was named: COLORDER, with the description: "Combination Lexicographical ORDER", version 1.00, July 2002 (2 WE). I want first to offer my algorithm to reputable repositories. I offered my previous algorithm to netlib.org. I don't know what was with them. I don't know how they handled my source code. Title: "Improve software to find combination lexicographical order". Improving NthIndex, the first software to calculate or find the lexicographic order or rank of a lotto combination; or find the combination for a given rank.

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