Biperiodic forests per homology -- q,t analogues (diagrams)

Values of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;1,1)\) on this page.
Values of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) as polynomials on this page.

For \(\theta = 0\)

0

1

0

	1
1	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,1)\)

0

1

2

0

	0	1
0		2
1	2

	2
2	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,2)\)

0

1

2

3

0

	0	1
0	3	3
1	3

	1	2
1		3
2	3

	3
3	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,3)\)

0

1

2

0

	0	1	2	3
0			2	4
1		8	4
2	2	4
3	4

	4
4	1

1

	0	1	2
0	8	8	2
1	8
2	2

	2
2	2

2

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (2,2)\)

0

1

2

3

4

0

	0	1
0	8	4
1	4

	0	1	2
0			2
1		8	4
2	2	4

	2	3
2		4
3	4

	4
4	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,4)\)

0

1

2

3

4

5

0

	0	1
0	15	5
1	5

	0	1	2
0		5	5
1	5	20	5
2	5	5

	1	2	3
1			5
2		15	5
3	5	5

	3	4
3		5
4	5

	5
5	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,5)\)

0

1

2

3

0

	0	1	2	3	4
0	3	30	51	24	12
1	30	60	42	6
2	51	42
3	24	6
4	12

	2	3	4	5
2			3	6
3		12	6
4	3	6
5	6

	6
6	1

1

	0	1	2	3
0	36	36	12	2
1	36	12
2	12
3	2

2

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (2,3)\)

0

1

2

3

4

5

6

0

	0	1
0	24	6
1	6

	0	1	2
0	3	18	9
1	18	36	6
2	9	6

	0	1	2	3
0				2
1			18	12
2		18	36	6
3	2	12	6

	2	3	4
2			9
3		24	6
4	9	6

	4	5
4		6
5	6

	6
6	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,6)\)

0

1

2

3

4

5

6

7

0

	0	1
0	35	7
1	7

	0	1	2
0	14	42	14
1	42	56	7
2	14	7

	0	1	2	3
0			7	7
1		21	63	21
2	7	63	63	7
3	7	21	7

	1	2	3	4
1				7
2			42	21
3		42	56	7
4	7	21	7

	3	4	5
3			14
4		35	7
5	14	7

	5	6
5		7
6	7

	7
7	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,7)\)

0

1

2

3

4

0

	0	1	2	3	4	5
0	88	336	420	280	96	32
1	336	640	400	120	8
2	420	400	96
3	280	120
4	96	8
5	32

	0	1	2	3	4	5	6
0					2	8	8
1				16	40	16
2			40	88	92	32	16
3		16	88	112	56	8
4	2	40	92	56
5	8	16	32	8
6	8		16

	4	5	6	7
4			4	8
5		16	8
6	4	8
7	8

	8
8	1

1

	0	1	2	3	4
0	136	160	72	16	2
1	160	96	16
2	72	16
3	16
4	2

	4
4	2

2

	0
0	1

	0	1	2	3	4
0			4	8	4
1		16	32	16	8
2	4	32	32
3	8	16
4	4	8

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (2,4)\)

0

1

2

3

4

5

6

7

8

0

	0	1
0	48	8
1	8

	0	1	2
0	40	80	20
1	80	80	8
2	20	8

	0	1	2	3
0		8	32	16
1	8	96	144	32
2	32	144	96	8
3	16	32	8

	0	1	2	3	4
0					2
1				32	24
2			72	144	36
3		32	144	96	8
4	2	24	36	8

	2	3	4	5
2				16
3			80	32
4		80	80	8
5	16	32	8

	4	5	6
4			20
5		48	8
6	20	8

	6	7
6		8
7	8

	8
8	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,8)\)

0

1

2

3

0

	0	1	2	3	4	5	6	7
0	3	63	270	462	405	243	81	27
1	63	468	819	684	306	99	9
2	270	819	819	333	63
3	462	684	333	54	9
4	405	306	63	9
5	243	99
6	81	9
7	27

	3	4	5	6	7	8
3				3	9	9
4			27	36	9
5		27	18	9
6	3	36	9
7	9	9
8	9

	9
9	1

1

	0	1	2	3	4	5	6
0	621	1143	918	432	135	27	3
1	1143	1359	630	153	18
2	918	630	153	18
3	432	153	18	3
4	135	18
5	27
6	3

	0	1	2	3	4	5	6
0				3	9	9	3
1			27	90	99	54	18
2		27	144	153	63
3	3	90	153	54	9
4	9	99	63	9
5	9	54
6	3	18

	6
6	3

2

	0	1	2	3
0	54	54	18	3
1	54	18
2	18
3	3

	3
3	3

3

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (3,3)\)

0

1

2

3

4

5

6

7

8

9

0

	0	1
0	63	9
1	9

	0	1	2
0	90	135	27
1	135	108	9
2	27	9

	0	1	2	3
0	3	45	90	30
1	45	270	270	45
2	90	270	135	9
3	30	45	9

	0	1	2	3	4
0				9	9
1			54	144	54
2		54	324	324	54
3	9	144	324	144	9
4	9	54	54	9

	1	2	3	4	5
1					9
2				90	54
3			180	270	54
4		90	270	135	9
5	9	54	54	9

	3	4	5	6
3				30
4			135	45
5		135	108	9
6	30	45	9

	5	6	7
5			27
6		63	9
7	27	9

	7	8
7		9
8	9

	9
9	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,9)\)

0

1

2

3

4

5

6

7

8

9

10

0

	0	1
0	80	10
1	10

	0	1	2
0	175	210	35
1	210	140	10
2	35	10

	0	1	2	3
0	20	150	200	50
1	150	600	450	60
2	200	450	180	10
3	50	60	10

	0	1	2	3	4
0			15	50	25
1		40	300	400	100
2	15	300	900	600	75
3	50	400	600	200	10
4	25	100	75	10

	0	1	2	3	4	5
0						2
1					50	40
2				200	400	120
3			200	800	600	80
4		50	400	600	200	10
5	2	40	120	80	10

	2	3	4	5	6
2					25
3				200	100
4			375	450	75
5		200	450	180	10
6	25	100	75	10

	4	5	6	7
4				50
5			210	60
6		210	140	10
7	50	60	10

	6	7	8
6			35
7		80	10
8	35	10

	8	9
8		10
9	10

	10
10	1

1

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (1,10)\)

0

1

2

3

4

0

	0	1	2	3	4	5	6	7	8	9
0	680	4368	11052	15436	14160	9324	4632	1764	468	108
1	4368	17784	29412	27228	16260	6732	1908	384	12
2	11052	29412	31800	18876	6876	1560	168
3	15436	27228	18876	6696	1332	132
4	14160	16260	6876	1332	120	12
5	9324	6732	1560	132	12
6	4632	1908	168
7	1764	384
8	468	12
9	108

	0	1	2	3	4	5	6	7	8	9	10
0							2	12	30	36	18
1						24	108	192	144	36
2					126	432	600	408	138
3				248	816	1236	1108	564	288	108	36
4			126	816	1548	1572	1002	372	120	12
5		24	432	1236	1572	1128	408	84
6	2	108	600	1108	1002	408	48	12
7	12	192	408	564	372	84	12
8	30	144	138	288	120
9	36	36		108	12
10	18			36

	6	7	8	9	10	11
6				4	12	12
7			36	48	12
8		36	24	12
9	4	48	12
10	12	12
11	12

	12
12	1

1

	0	1	2	3	4	5	6	7	8
0	7164	15528	15342	9240	3816	1140	246	36	3
1	15528	24768	17364	7092	1848	300	24
2	15342	17364	8316	2196	336	24
3	9240	7092	2196	336	24
4	3816	1848	336	24	3
5	1140	300	24
6	246	24
7	36
8	3

2

	0	1	2	3	4
0	204	240	108	24	3
1	240	144	24
2	108	24
3	24
4	3

	4	5	6	7	8
4			30	60	30
5		72	60
6	30	60	48
7	60
8	30

3

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (3,4)\)

0

1

2

3

4

0

	0	1	2	3	4	5	6	7	8	9	10	11	12	13
0	5176	46768	173600	369376	523988	543744	437384	282752	149696	65152	23280	6704	1472	256
1	46768	300704	806464	1256592	1314672	1005456	590192	272624	99344	28144	5936	880	16
2	173600	806464	1583136	1809376	1381856	762608	315928	99280	22840	3600	256
3	369376	1256592	1809376	1506752	829360	324640	92768	19024	2496	176
4	523988	1314672	1381856	829360	325088	89456	17600	2384	208	16
5	543744	1005456	762608	324640	89456	17440	2416	224	16
6	437384	590192	315928	92768	17600	2416	192
7	282752	272624	99280	19024	2384	224
8	149696	99344	22840	2496	208	16
9	65152	28144	3600	176	16
10	23280	5936	256
11	6704	880
12	1472	16
13	256

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
0									2	16	56	112	136	96	32
1								32	208	576	880	768	352	64
2							256	1328	2920	3568	2592	1120	240
3						992	4352	8464	9728	7168	3264	880	160
4					1672	7584	16000	19936	16148	9120	4160	1760	784	256	64
5				992	7584	19680	27392	24384	15216	7216	3024	976	224	16
6			256	4352	16000	27392	28048	19088	9168	3232	792	112
7		32	1328	8464	19936	24384	19088	9504	3072	704	96	16
8	2	208	2920	9728	16148	15216	9168	3072	736	128	16
9	16	576	3568	7168	9120	7216	3232	704	128
10	56	880	2592	3264	4160	3024	792	96	16
11	112	768	1120	880	1760	976	112	16
12	136	352	240	160	784	224
13	96	64			256	16
14	32				64

	8	9	10	11	12	13	14	15
8					4	16	24	16
9				64	144	96	16
10			144	160	56	16
11		64	160	128	16
12	4	144	56	16
13	16	96	16
14	24	16
15	16

	16
16	1

1

	0	1	2	3	4	5	6	7	8	9	10	11	12
0	270720	844736	1251248	1177424	795320	412384	170576	57296	15624	3392	560	64	4
1	844736	2137472	2529168	1872448	978576	384080	116336	27120	4688	544	32
2	1251248	2529168	2353824	1349856	537496	157216	34264	5424	576	32
3	1177424	1872448	1349856	590592	176624	37840	5744	576	32
4	795320	978576	537496	176624	39184	6048	632	48	4
5	412384	384080	157216	37840	6048	608	32
6	170576	116336	34264	5744	632	32
7	57296	27120	5424	576	48
8	15624	4688	576	32	4
9	3392	544	32
10	560	32
11	64
12	4

	0	1	2	3	4	5	6	7	8	9	10	11	12
0	4	240	2568	11072	26044	38960	40632	31248	18252	8144	2688	608	76
1	240	5696	35168	98272	157328	164560	122048	67392	28192	8992	2160	384	48
2	2568	35168	140688	267424	299336	220848	115256	44112	12288	2384	256
3	11072	98272	267424	354784	278224	142496	50704	12528	2016	192
4	26044	157328	299336	278224	150196	51808	12200	1888	192	16
5	38960	164560	220848	142496	51808	12288	2128	240	32
6	40632	122048	115256	50704	12200	2128	256
7	31248	67392	44112	12528	1888	240
8	18252	28192	12288	2016	192	32
9	8144	8992	2384	192	16
10	2688	2160	256
11	608	384
12	76	48

	4	5	6	7	8	9	10	11	12
4					76	304	456	304	76
5				448	1344	1440	688	192	48
6			800	2176	2360	1408	384
7		448	2176	3008	1488	224	32
8	76	1344	2360	1488	496	16
9	304	1440	1408	224	16
10	456	688	384	32
11	304	192
12	76	48

	12
12	4

2

	0	1	2	3	4	5	6	7	8
0	18768	42256	42800	25904	10496	2992	600	80	6
1	42256	71072	51760	21392	5472	848	64
2	42800	51760	25840	6768	976	64
3	25904	21392	6768	960	64
4	10496	5472	976	64	8
5	2992	848	64
6	600	64
7	80
8	6

	0	1	2	3	4	5	6	7	8
0					4	16	24	16	4
1				64	288	480	400	192	48
2			144	928	1952	1936	1008	288	72
3		64	928	2816	3088	1584	416
4	4	288	1952	3088	1792	384	32
5	16	480	1936	1584	384	32
6	24	400	1008	416	32
7	16	192	288
8	4	48	72

	8
8	6

3

	0	1	2	3	4
0	272	320	144	32	4
1	320	192	32
2	144	32
3	32
4	4

	4
4	4

4

	0
0	1

Value of \([w^{ki}z^{kj}]T_{\vec{\theta},W\times H}(w,z;q,t)\) for \((W,H) = (4,4)\)