GCP and LCS of 2 pawn structures

Sort:
Yigor

Definition 1. Suppose that we have 2 different legal pawn structures P1 and P2. P1 will be called a predecessor of P2 and P2 a successor of P1 if there exist legal positions A and B with pawn structures P1 and P2 respectively such that B can be obtained from A by a sequence of legal moves.

 

The notion of pawn height is introduced here:

https://www.chess.com/forum/view/chess-openings/pawn-structure-classification-codes

 

Definition 2. Let P1 and P2 be 2 pawn structures. The greatest common predecessor GCP(P1,P2) is the predecessor of both P1 and P2 having the highest pawn height. The least common successor  LCS(P1,P2) is the heritor of both P1 and P2 having the lowest pawn height.

 

Example 1. Let P1=2Ec Sicilian Defense and P2=2E1e French Defense  then

GCP(2Ec, 2E1e) = 2E King's Pawn Opening,

LCS(2Ec, 2E1e) = 2Ec1e Sicilian Defense: French Variation.

 

 

It's a good way to give names to unnamed opennings. happy.png

 

Example 2. Let P1=2DEe Scotch game and P2=2Ee1d Philidor Defense  then

LCS(2DEe, 2Ee1d) = 2DEe1d

can be called Scotch Game: Philidor Variation. gold.png

 

 

Sqod
Yigor wrote:
Example 1. Let P1=2EcSicilian Defense and P2=2E1e French Defense  then

GCP(2Ec, 2E1e) = 2E King's Pawn Opening,

LCH(2Ec, 2E1e) = 2Ec1e Sicilian Defense: French Variation.

You didn't explain your 3-digit/4-digit/5-digit notation. I figured it out, but most readers aren't going to go to the trouble to do that.

One major problem with this whole idea is that human brains don't remember things well when they're written with letters and numbers. For example, one database shows one opening called "Queen's Gambit Declined, 4.Bg5 Be7." Get real! Can you imagine trying to remember, pronounce, or interpret the spoken name of that opening? I guess one would say: "Queen's Gambit Declined Four Bee GeeFive Bee EeSeven." It gives me a headache to even look at that.

I came up with what I believe is a better scheme where I use 3-letter mnemonics for each move. For example:

...a6 = -naj- <= Najdorf Sicilian
...e6 = -fre- <= French Defense
...h6 = -lev- <= Levitsky Attack

Nb3 = -bol- <= Boleslavsky Sicilian
Nc3 = -dun- <= Dunst Opening
Nd2 = -tar- <= Tarrasch French

Therefore if a variation involved the moves Nc3 ...a6 together, I would call it the Dunnaj Variation. That's very pronounceable, and those mnemonics are usually concatenatable. That method has the drawback of a huge number of theoretical piece-square combinations, but in practice only a manageably small number of those possibilities is commonly used. I've been using that system without much trouble for the past year.

Yigor

Sqod:  Well, my mathematical PSCC notations are suitable to calculate pawn height, write formulas and so on. Your mnemonic notations might be good to memorize openings. Anyway, the notions of  GCP and LCH don't depend on notations. They are similar to GCD and LCM in arithmetics. happy.png

Sqod
Yigor wrote:

Sqod:  Well, my mathematical PSCC notations are suitable to calculate pawn height, write formulas and so on. Your mnemonic notations might be good to memorize openings. Anyway, the notions of  GCP and LCH don't depend on notations. They are similar to GCD and LCM in arithmetics.

Agreed.

You didn't state your goal, so it wasn't clear to me why you were doing this work, other than you suggesting it would be useful for giving names to openings, so I took that to be one of your primary goals.

So what *is* your primary goal of this work? I think this might be useful for pattern recognition purposes, but did you have something else in mind?

Yigor

Sqod: As U said, pattern recognition, classification and naming. No other goals at the moment.

Intermediatedinoz: The life of a poet isn't easy. wink.png

BronsteinPawn

Chess is not rocket science,I dont need these.

Yigor
BronsteinPawn wrote:

Chess is not rocket science, I dont need these.

 

LoL Well, personally I like rockets and cosmonautics. bullet.pnghappy.png

 

U wanted a definition and I gave it. settings.png

Yigor

Btw, one more example: Dragodorf = LCS(Dragon, Najdorf). chessbook.png