Djeneba Diop - cp's OEIS frontend

User: Djeneba Diop

Djeneba Diop has authored 4 sequences.

A364480 Table of Sprague-Grundy values for M X N Pop-It! hooks read by antidiagonals.

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 1, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 1, 9, 9, 9, 9, 10, 10, 10, 10, 2, 2, 10, 10, 10, 10, 11, 11, 11, 11, 3, 3, 3, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

Offset: 1

Ryan J. Blau, Michael Carrion, Djeneba Diop, Sarah Dumnich, Matt Prudente, and Nathan B. Shank, Jul 26 2023

Pop-It! is played on an M X N lattice graph with a "pip" at each node. A move consists of popping any number of pips that are all collinear on the same horizontal or vertical line. A hook h(a,b) is defined as two lines of lengths a and b connected by a corner pip. The total number of pips of a hook h(a,b) is a+b+1.

This table seems to have similarities to A354586.

			Table begins
   1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
   2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
   3,  4,  1,  6,  7,  8,  9, 10, 11, 12, 13, ...
   4,  5,  6,  7,  8,  9, 10, 11, 12, 13, ...
   5,  6,  7,  8,  1,  2,  3, 12, 13, ...
   6,  7,  8,  9,  2,  3, 12, 13, ...
   7,  8,  9, 10,  3, 12,  1, ...
   8,  9, 10, 11, 12, 13, ...
   9, 10, 11, 12, 13, ...
  10, 11, 12, 13, ...
  11, 12, 13, ...
  12, 13, ...
  13, ...
  ...

Ryan J. Blau, Colored pattern of hook Sprague-Grundy values.
Ryan J. Blau, Python Code.

Sprague-Grundy values for Toppling Dominoes L's: A354586.

Cf. A038712 (main diagonal).

A364503 Sprague-Grundy values for Heat-Charge Toggle on paths from A364489 where paths with an even number of vertices are odious, or paths with an odd number of vertices are evil.

Original entry on oeis.org

0, 2, 1, 3, 2, 2, 3, 4, 5, 3, 7, 3, 4, 4, 6, 5, 5, 6, 4, 7, 6, 3, 10, 4, 16, 18, 16, 32, 32, 32, 32, 32, 36, 32, 36, 32, 33, 36, 32, 33, 32, 32, 32, 35, 33, 34, 34, 36, 35, 33, 33, 32, 36, 32, 33, 32, 36, 34, 34, 37, 37, 34

Offset: 1

Jean-Pierre Appel, Patrick G. Cesarz, Djeneba Diop, Eugene Fiorini, Nathan Hurtig, Andrew Woldar, Jul 26 2023

See A364489 for the rules of Heat-Charge Toggle.

			a(2) = 2, which is odious. So the second term of A364489 is an even number.

E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.

Nathan Hurtig, C++ program to compute values

Cf. A000069, A001969, A363934. Sprague-Grundy values of A364489.

A364489 Values of n for which the Sprague-Grundy value of Heat-Charge Toggle on an (n+2)-vertex path with initial weights -1,1^n,-1 is evil for odd n or odious for even n.

Original entry on oeis.org

1, 4, 6, 9, 14, 22, 27, 30, 35, 41, 58, 59, 72, 84, 87, 89, 103, 105, 108, 124, 129, 141, 171, 258, 284, 407, 458, 11770548, 25146268, 27690032, 41693544, 55788270, 74838555, 86120064, 89811321, 95580294, 119784327, 139336981, 158776090, 160066751, 161102638, 181691114, 186919128

Offset: 1

Jean-Pierre Appel, Patrick G. Cesarz, Djeneba Diop, Eugene Fiorini, Nathan Hurtig, Andrew Woldar, Jul 26 2023

nonn

Heat-Charge Toggle is an impartial two-player game on a finite simple graph, where each vertex is assigned a weight of -1, 0, or 1.
A Heat-Charge Toggle move consists of selecting a vertex of weight 1 and switching its weight to 0, as well as switching the sign of each of its neighbors: changing 1 to -1, -1 to 1, and keeping 0 at 0.
We additionally only allow moves that strictly decrease the sum of all weights.
The two vertices of degree one have initial weights of -1, while vertices of degree two have an initial weight of 1.

			For n = 4, the Sprague-Grundy value for a 6-vertex path is 2.
Note that n = 4 is even and 2 is odious (see A000069).

E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.

Nathan Hurtig, C++ program to compute values

Cf. A000069, A001969, A361517, A363934. Paths with Sprague-Grundy values A364503.

A363934 Table read by ascending antidiagonals. T(n,k) is the Sprague-Grundy value for the Heat Toggle game played on an n X k grid where each vertex has initial weight 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 1, 0, 2, 0, 3, 1, 1, 3, 0, 3, 1, 3, 0, 3, 1, 3, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0, 3, 2, 2, 3, 1, 1

Offset: 1

Jean-Pierre Appel, Patrick G. Cesarz, Djeneba Diop, Eugene Fiorini, Nathan Hurtig, Andrew Woldar, Jun 28 2023

Heat Toggle is an impartial two-player game played on a simple graph, where each vertex is assigned a weight of -1 or 1.
A Heat Toggle move consists of selecting a vertex of weight 1 and switching its weight to -1 as well as switching the weight of each of its neighbors, changing 1 to -1 and -1 to 1. We additionally only allow moves that strictly decrease the sum of all weights.
The first row T(1,k) coincides with octal game 0.1337, see A071427.
The second row T(2,k) coincides with the octal game 0.137 (Dawson's Chess), see A002187.

			The data is organized in a table beginning with row n = 1 and column k = 1. The data is read by ascending antidiagonals. T(2,3)=2.
The table T(n,k) begins:
[n/k]  1   2   3   4   5   6  ...
---------------------------------
[1]    1,  1,  1,  2,  2,  0, ...
[2]    1,  1,  2,  0,  3,  1, ...
[3]    1,  2,  1,  1,  3,  0, ...
[4]    2,  0,  1,  0,  1,  0, ...
[5]    2,  3,  3,  1,  2,  0, ...
[6]    0,  1,  0,  0,  0,  ...

E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.

E. Fiorini, M. Lind, A. Woldar, and T. W. H. Wong, Characterizing Winning Positions in the Impartial Two-player Pebbling Game on Complete Graphs, Journal of Integer Sequences 24(6), (2021).

Cf. A361517, A071427, A002187.

SG_value_hash = {}
def MEX(S):
    i = 0
    while True:
        if i not in S:
            return i
        i += 1
def SG_value(G):
    global SG_value_hash
    SG_value_hash = {}
    ons = set(G.vertices())
    offs = set()
    return SG_value_helper(G, ons, offs)
def SG_value_helper(G, ons, offs):
    ons_orig = ons.copy()
    offs_orig = offs.copy()
    child_SG_values = set()
    for v in ons_orig:
        vNeighborhood = set(G.neighbors(v))
        neighNowOff = ons_orig.intersection(vNeighborhood)
        neighNowOn = offs_orig.intersection(vNeighborhood)
        if len(neighNowOff) >= len(neighNowOn):
            ons.remove(v)
            offs.add(v)
            ons.update(neighNowOn)
            offs -= neighNowOn
            offs.update(neighNowOff)
            ons -= neighNowOff
            result = -1 # placeholder
            encoded_position = str(offs)
            if encoded_position in SG_value_hash:
                result = SG_value_hash[encoded_position]
            else:
                result = SG_value_helper(G, ons, offs)
            SG_value_hash[encoded_position] = result
            ons.add(v)
            offs.remove(v)
            ons -= neighNowOn
            offs.update(neighNowOn)
            offs -= neighNowOff
            ons.update(neighNowOff)
            child_SG_values.add(result)
    return MEX(child_SG_values)
for sum_of_both in range(2,11):
    antidiagonal = []
    for n in range(1, sum_of_both):
        G = graphs.Grid2dGraph(n, sum_of_both-n)
        antidiagonal.append(SG_value(G))
    print(antidiagonal)

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User: Djeneba Diop

A364480 Table of Sprague-Grundy values for M X N Pop-It! hooks read by antidiagonals.

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A364503 Sprague-Grundy values for Heat-Charge Toggle on paths from A364489 where paths with an even number of vertices are odious, or paths with an odd number of vertices are evil.

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A364489 Values of n for which the Sprague-Grundy value of Heat-Charge Toggle on an (n+2)-vertex path with initial weights -1,1^n,-1 is evil for odd n or odious for even n.

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A363934 Table read by ascending antidiagonals. T(n,k) is the Sprague-Grundy value for the Heat Toggle game played on an n X k grid where each vertex has initial weight 1.

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